From 685638d7de817b9f6529fd481fc62603aa6c4986 Mon Sep 17 00:00:00 2001 From: Udoh Jeremiah Date: Tue, 6 Jun 2023 00:15:03 +0100 Subject: [PATCH] update old problems and add new ones --- src/P1/problem.jl | 2 +- src/P10/problem.jl | 2 +- src/P100/problem.jl | 2 +- src/P101/problem.jl | 2 +- src/P102/problem.jl | 2 +- src/P103/problem.jl | 2 +- src/P104/problem.jl | 2 +- src/P105/problem.jl | 2 +- src/P106/problem.jl | 2 +- src/P107/problem.jl | 2 +- src/P108/problem.jl | 2 +- src/P109/problem.jl | 2 +- src/P11/problem.jl | 2 +- src/P110/problem.jl | 2 +- src/P111/problem.jl | 2 +- src/P112/problem.jl | 2 +- src/P113/problem.jl | 2 +- src/P114/problem.jl | 2 +- src/P115/problem.jl | 2 +- src/P116/problem.jl | 2 +- src/P117/problem.jl | 2 +- src/P118/problem.jl | 2 +- src/P119/problem.jl | 2 +- src/P12/problem.jl | 2 +- src/P120/problem.jl | 2 +- src/P121/problem.jl | 2 +- src/P122/problem.jl | 2 +- src/P123/problem.jl | 2 +- src/P124/problem.jl | 2 +- src/P125/problem.jl | 2 +- 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src/P732/problem.jl | 2 +- src/P733/problem.jl | 2 +- src/P734/problem.jl | 2 +- src/P735/problem.jl | 2 +- src/P736/problem.jl | 2 +- src/P737/problem.jl | 2 +- src/P738/problem.jl | 2 +- src/P739/problem.jl | 2 +- src/P74/problem.jl | 2 +- src/P740/problem.jl | 2 +- src/P741/problem.jl | 2 +- src/P742/problem.jl | 2 +- src/P743/problem.jl | 2 +- src/P744/problem.jl | 2 +- src/P745/problem.jl | 2 +- src/P746/problem.jl | 2 +- src/P747/problem.jl | 2 +- src/P748/problem.jl | 2 +- src/P749/problem.jl | 2 +- src/P75/problem.jl | 2 +- src/P750/problem.jl | 2 +- src/P751/problem.jl | 2 +- src/P752/problem.jl | 2 +- src/P753/problem.jl | 2 +- src/P754/problem.jl | 2 +- src/P755/problem.jl | 2 +- src/P756/problem.jl | 2 +- src/P757/problem.jl | 2 +- src/P758/problem.jl | 2 +- src/P759/problem.jl | 2 +- src/P76/problem.jl | 2 +- src/P760/problem.jl | 2 +- src/P761/problem.jl | 2 +- src/P762/problem.jl | 2 +- src/P763/problem.jl | 2 +- src/P764/problem.jl | 2 +- src/P765/problem.jl | 2 +- src/P766/problem.jl | 2 +- src/P767/problem.jl | 2 +- src/P768/problem.jl | 2 +- src/P769/problem.jl | 2 +- src/P77/problem.jl | 2 +- src/P770/problem.jl | 2 +- src/P771/problem.jl | 2 +- src/P772/problem.jl | 2 +- src/P773/problem.jl | 2 +- src/P774/problem.jl | 2 +- src/P775/problem.jl | 2 +- src/P776/problem.jl | 2 +- src/P777/problem.jl | 2 +- src/P778/problem.jl | 2 +- src/P779/problem.jl | 2 +- src/P78/problem.jl | 2 +- src/P780/problem.jl | 2 +- src/P781/problem.jl | 2 +- src/P783/problem.jl | 2 +- src/P784/problem.jl | 2 +- src/P785/problem.jl | 2 +- src/P786/problem.jl | 2 +- src/P787/problem.jl | 2 +- src/P788/problem.jl | 2 +- src/P789/problem.jl | 2 +- src/P79/problem.jl | 2 +- src/P790/problem.jl | 2 +- src/P791/problem.jl | 2 +- src/P792/problem.jl | 2 +- src/P793/problem.jl | 2 +- src/P794/problem.jl | 2 +- src/P795/problem.jl | 2 +- src/P796/problem.jl | 2 +- src/P797/problem.jl | 2 +- src/P798/problem.jl | 2 +- src/P799/problem.jl | 2 +- src/P8/problem.jl | 2 +- src/P80/problem.jl | 2 +- src/P800/problem.jl | 2 +- src/P801/problem.jl | 2 +- src/P802/problem.jl | 2 +- src/P803/problem.jl | 2 +- src/P804/problem.jl | 2 +- src/P805/problem.jl | 2 +- src/P806/problem.jl | 2 +- src/P807/problem.jl | 2 +- src/P808/problem.jl | 2 +- src/P809/problem.jl | 2 +- src/P81/problem.jl | 2 +- src/P810/problem.jl | 2 +- src/P811/problem.jl | 2 +- src/P812/problem.jl | 2 +- src/P813/problem.jl | 2 +- src/P814/problem.jl | 2 +- src/P815/problem.jl | 2 +- src/P816/problem.jl | 2 +- src/P817/problem.jl | 2 +- src/P818/problem.jl | 2 +- src/P819/problem.jl | 2 +- src/P82/problem.jl | 2 +- src/P820/problem.jl | 2 +- src/P821/problem.jl | 2 +- src/P822/problem.jl | 2 +- src/P823/problem.jl | 2 +- src/P824/problem.jl | 2 +- src/P825/problem.jl | 2 +- src/P826/problem.jl | 2 +- src/P827/problem.jl | 2 +- src/P828/problem.jl | 2 +- src/P829/problem.jl | 2 +- src/P83/problem.jl | 2 +- src/P830/problem.jl | 2 +- src/P831/problem.jl | 4 ++-- src/P832/problem.jl | 4 ++-- src/P833/problem.jl | 4 ++-- src/P834/problem.jl | 4 ++-- src/P835/problem.jl | 4 ++-- src/P836/problem.jl | 4 ++-- src/P837/problem.jl | 2 +- src/P838/problem.jl | 2 +- src/P839/problem.jl | 2 +- src/P84/problem.jl | 2 +- src/P840/problem.jl | 2 +- src/P841/problem.jl | 30 ++++++++++++++++++++++++++++++ src/P842/problem.jl | 27 +++++++++++++++++++++++++++ src/P843/problem.jl | 24 ++++++++++++++++++++++++ src/P844/problem.jl | 28 ++++++++++++++++++++++++++++ src/P845/problem.jl | 16 ++++++++++++++++ src/P846/problem.jl | 29 +++++++++++++++++++++++++++++ src/P85/problem.jl | 2 +- src/P86/problem.jl | 2 +- src/P87/problem.jl | 2 +- src/P88/problem.jl | 2 +- src/P89/problem.jl | 2 +- src/P9/problem.jl | 2 +- src/P90/problem.jl | 2 +- src/P91/problem.jl | 2 +- src/P92/problem.jl | 2 +- src/P93/problem.jl | 2 +- src/P94/problem.jl | 2 +- src/P95/problem.jl | 2 +- src/P96/problem.jl | 2 +- src/P97/problem.jl | 2 +- src/P98/problem.jl | 2 +- src/P99/problem.jl | 2 +- src/problemfiles.jl | 6 ++++++ src/unedited_questions.txt | 4 ++++ 803 files changed, 965 insertions(+), 801 deletions(-) create mode 100644 src/P841/problem.jl create mode 100644 src/P842/problem.jl create mode 100644 src/P843/problem.jl create mode 100644 src/P844/problem.jl create mode 100644 src/P845/problem.jl create mode 100644 src/P846/problem.jl diff --git a/src/P1/problem.jl b/src/P1/problem.jl index c772f87..2178def 100644 --- a/src/P1/problem.jl +++ b/src/P1/problem.jl @@ -3,7 +3,7 @@ module Problem1 title = "Problem 1: Multiples of 3 or 5" published_on = "Friday, 5th October 2001, 06:00 pm" -solved_by = 970042 +solved_by = 970256 difficulty_rating = "5%" content = """ If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. diff --git a/src/P10/problem.jl b/src/P10/problem.jl index c330bec..cc541bf 100644 --- a/src/P10/problem.jl +++ b/src/P10/problem.jl @@ -3,7 +3,7 @@ module Problem10 title = "Problem 10: Summation of primes" published_on = "Friday, 8th February 2002, 06:00 pm" -solved_by = 334328 +solved_by = 334541 difficulty_rating = "5%" content = """ The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. diff --git a/src/P100/problem.jl b/src/P100/problem.jl index 2b86f7c..90a3258 100644 --- a/src/P100/problem.jl +++ b/src/P100/problem.jl @@ -3,7 +3,7 @@ module Problem100 title = "Problem 100: Arranged probability" published_on = "Friday, 15th July 2005, 06:00 pm" -solved_by = 17044 +solved_by = 17092 difficulty_rating = "30%" content = """ If a box contains twenty-one coloured discs, composed of fifteen blue discs and six red discs, and two discs were taken at diff --git a/src/P101/problem.jl b/src/P101/problem.jl index fe16d7c..5b63956 100644 --- a/src/P101/problem.jl +++ b/src/P101/problem.jl @@ -3,7 +3,7 @@ module Problem101 title = "Problem 101: Optimum polynomial" published_on = "Friday, 29th July 2005, 06:00 pm" -solved_by = 12016 +solved_by = 12055 difficulty_rating = "35%" content = """ If we are presented with the first k terms of a sequence it is impossible to say with certainty the value of the next term, as there diff --git a/src/P102/problem.jl b/src/P102/problem.jl index 711afd8..405c420 100644 --- a/src/P102/problem.jl +++ b/src/P102/problem.jl @@ -3,7 +3,7 @@ module Problem102 title = "Problem 102: Triangle containment" published_on = "Friday, 12th August 2005, 06:00 pm" -solved_by = 22796 +solved_by = 22843 difficulty_rating = "15%" content = """ Three distinct points are plotted at random on a Cartesian plane, for which -1000 ≤ x, y ≤ 1000, such that a triangle is formed. diff --git a/src/P103/problem.jl b/src/P103/problem.jl index 313c08a..caf3cc7 100644 --- a/src/P103/problem.jl +++ b/src/P103/problem.jl @@ -3,7 +3,7 @@ module Problem103 title = "Problem 103: Special subset sums: optimum" published_on = "Friday, 26th August 2005, 06:00 pm" -solved_by = 8397 +solved_by = 8430 difficulty_rating = "45%" content = """ Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint diff --git a/src/P104/problem.jl b/src/P104/problem.jl index 612e540..0fe8792 100644 --- a/src/P104/problem.jl +++ b/src/P104/problem.jl @@ -3,7 +3,7 @@ module Problem104 title = "Problem 104: Pandigital Fibonacci ends" published_on = "Friday, 9th September 2005, 06:00 pm" -solved_by = 16805 +solved_by = 16838 difficulty_rating = "25%" content = """ The Fibonacci sequence is defined by the recurrence relation: diff --git a/src/P105/problem.jl b/src/P105/problem.jl index dd535fc..5797210 100644 --- a/src/P105/problem.jl +++ b/src/P105/problem.jl @@ -3,7 +3,7 @@ module Problem105 title = "Problem 105: Special subset sums: testing" published_on = "Friday, 23rd September 2005, 06:00 pm" -solved_by = 8379 +solved_by = 8400 difficulty_rating = "45%" content = """ Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint diff --git a/src/P106/problem.jl b/src/P106/problem.jl index 849c838..8bc223e 100644 --- a/src/P106/problem.jl +++ b/src/P106/problem.jl @@ -3,7 +3,7 @@ module Problem106 title = "Problem 106: Special subset sums: meta-testing" published_on = "Friday, 7th October 2005, 06:00 pm" -solved_by = 6687 +solved_by = 6701 difficulty_rating = "50%" content = """ Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint diff --git a/src/P107/problem.jl b/src/P107/problem.jl index d5d1d0a..39a1e92 100644 --- a/src/P107/problem.jl +++ b/src/P107/problem.jl @@ -3,7 +3,7 @@ module Problem107 title = "Problem 107: Minimal network" published_on = "Friday, 21st October 2005, 06:00 pm" -solved_by = 11446 +solved_by = 11472 difficulty_rating = "35%" content = """ The following undirected network consists of seven vertices and twelve edges with a total weight of 243. diff --git a/src/P108/problem.jl b/src/P108/problem.jl index 81979b6..41c7e6e 100644 --- a/src/P108/problem.jl +++ b/src/P108/problem.jl @@ -3,7 +3,7 @@ module Problem108 title = "Problem 108: Diophantine reciprocals I" published_on = "Friday, 4th November 2005, 06:00 pm" -solved_by = 13102 +solved_by = 13144 difficulty_rating = "30%" content = """ In the following equation diff --git a/src/P109/problem.jl b/src/P109/problem.jl index 916f6f1..597f4e3 100644 --- a/src/P109/problem.jl +++ b/src/P109/problem.jl @@ -3,7 +3,7 @@ module Problem109 title = "Problem 109: Darts" published_on = "Friday, 18th November 2005, 06:00 pm" -solved_by = 8476 +solved_by = 8499 difficulty_rating = "45%" content = """ In the game of darts a player throws three darts at a target board which is split into twenty equal sized sections numbered one to twenty. diff --git a/src/P11/problem.jl b/src/P11/problem.jl index e41511a..37a01fe 100644 --- a/src/P11/problem.jl +++ b/src/P11/problem.jl @@ -3,7 +3,7 @@ module Problem11 title = "Problem 11: Largest product in a grid" published_on = "Friday, 22nd February 2002, 06:00 pm" -solved_by = 240541 +solved_by = 240754 difficulty_rating = "5%" content = """ In the 20×20 grid below, four numbers along a diagonal line have been marked in red. diff --git a/src/P110/problem.jl b/src/P110/problem.jl index 419ca94..759a7a9 100644 --- a/src/P110/problem.jl +++ b/src/P110/problem.jl @@ -3,7 +3,7 @@ module Problem110 title = "Problem 110: Diophantine reciprocals II" published_on = "Friday, 2nd December 2005, 06:00 pm" -solved_by = 8413 +solved_by = 8440 difficulty_rating = "40%" content = """ In the following equation diff --git a/src/P111/problem.jl b/src/P111/problem.jl index 7318f78..73b8f91 100644 --- a/src/P111/problem.jl +++ b/src/P111/problem.jl @@ -3,7 +3,7 @@ module Problem111 title = "Problem 111: Primes with runs" published_on = "Friday, 16th December 2005, 06:00 pm" -solved_by = 7546 +solved_by = 7569 difficulty_rating = "45%" content = """ Considering 4-digit primes containing repeated digits it is clear that they cannot all be the same: 1111 is divisible by 11, 2222 is diff --git a/src/P112/problem.jl b/src/P112/problem.jl index 3a69b82..02b0f07 100644 --- a/src/P112/problem.jl +++ b/src/P112/problem.jl @@ -3,7 +3,7 @@ module Problem112 title = "Problem 112: Bouncy numbers" published_on = "Friday, 30th December 2005, 06:00 pm" -solved_by = 25462 +solved_by = 25512 difficulty_rating = "15%" content = """ Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. diff --git a/src/P113/problem.jl b/src/P113/problem.jl index fad2b5c..6f5316b 100644 --- a/src/P113/problem.jl +++ b/src/P113/problem.jl @@ -3,7 +3,7 @@ module Problem113 title = "Problem 113: Non-bouncy numbers" published_on = "Friday, 10th February 2006, 06:00 pm" -solved_by = 11488 +solved_by = 11513 difficulty_rating = "30%" content = """ Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. diff --git a/src/P114/problem.jl b/src/P114/problem.jl index 172551c..38c4b5b 100644 --- a/src/P114/problem.jl +++ b/src/P114/problem.jl @@ -3,7 +3,7 @@ module Problem114 title = "Problem 114: Counting block combinations I" published_on = "Friday, 17th February 2006, 06:00 pm" -solved_by = 11239 +solved_by = 11266 difficulty_rating = "35%" content = """ A row measuring seven units in length has red blocks with a minimum length of three units placed on it, such that any two red diff --git a/src/P115/problem.jl b/src/P115/problem.jl index 6e3ab7f..056a5d0 100644 --- a/src/P115/problem.jl +++ b/src/P115/problem.jl @@ -3,7 +3,7 @@ module Problem115 title = "Problem 115: Counting block combinations II" published_on = "Friday, 24th February 2006, 06:00 pm" -solved_by = 10277 +solved_by = 10301 difficulty_rating = "35%" content = """ NOTE: This is a more difficult version of \e[1;35mProblem 114\e[0m. diff --git a/src/P116/problem.jl b/src/P116/problem.jl index a8a30bb..30fa359 100644 --- a/src/P116/problem.jl +++ b/src/P116/problem.jl @@ -3,7 +3,7 @@ module Problem116 title = "Problem 116: Red, green or blue tiles" published_on = "Friday, 3rd March 2006, 06:00 pm" -solved_by = 12559 +solved_by = 12595 difficulty_rating = "30%" content = """ A row of five grey square tiles is to have a number of its tiles replaced with coloured oblong tiles chosen from red (length two), diff --git a/src/P117/problem.jl b/src/P117/problem.jl index b8ecc7f..5049572 100644 --- a/src/P117/problem.jl +++ b/src/P117/problem.jl @@ -3,7 +3,7 @@ module Problem117 title = "Problem 117: Red, green, and blue tiles" published_on = "Friday, 10th March 2006, 06:00 pm" -solved_by = 11529 +solved_by = 11566 difficulty_rating = "35%" content = """ Using a combination of grey square tiles and oblong tiles chosen from: red tiles (measuring two units), green tiles (measuring diff --git a/src/P118/problem.jl b/src/P118/problem.jl index 1ced507..ed03c76 100644 --- a/src/P118/problem.jl +++ b/src/P118/problem.jl @@ -3,7 +3,7 @@ module Problem118 title = "Problem 118: Pandigital prime sets" published_on = "Friday, 24th March 2006, 06:00 pm" -solved_by = 7267 +solved_by = 7289 difficulty_rating = "45%" content = """ Using all of the digits 1 through 9 and concatenating them freely to form decimal integers, different sets can be formed. diff --git a/src/P119/problem.jl b/src/P119/problem.jl index fa35019..1df62f5 100644 --- a/src/P119/problem.jl +++ b/src/P119/problem.jl @@ -3,7 +3,7 @@ module Problem119 title = "Problem 119: Digit power sum" published_on = "Friday, 7th April 2006, 06:00 pm" -solved_by = 12810 +solved_by = 12846 difficulty_rating = "30%" content = """ The number 512 is interesting because it is equal to the sum of its digits raised to some power: 5 + 1 + 2 = 8, and 8³ = 512. diff --git a/src/P12/problem.jl b/src/P12/problem.jl index 83815e5..81b44ef 100644 --- a/src/P12/problem.jl +++ b/src/P12/problem.jl @@ -3,7 +3,7 @@ module Problem12 title = "Problem 12: Highly divisible triangular number" published_on = "Friday, 8th March 2002, 06:00 pm" -solved_by = 227182 +solved_by = 227396 difficulty_rating = "5%" content = """ The sequence of triangle numbers is generated by adding the natural numbers. So the 7ᵗʰ triangle number would be 1 + 2 + 3 diff --git a/src/P120/problem.jl b/src/P120/problem.jl index f72b6e9..8fa216d 100644 --- a/src/P120/problem.jl +++ b/src/P120/problem.jl @@ -3,7 +3,7 @@ module Problem120 title = "Problem 120: Square remainders" published_on = "Friday, 21st April 2006, 06:00 pm" -solved_by = 14280 +solved_by = 14318 difficulty_rating = "25%" content = """ Let r be the remainder when (a-1)ⁿ + (a+1)ⁿ is divided by a². diff --git a/src/P121/problem.jl b/src/P121/problem.jl index 48ad1ea..40a4bc8 100644 --- a/src/P121/problem.jl +++ b/src/P121/problem.jl @@ -3,7 +3,7 @@ module Problem121 title = "Problem 121: Disc game prize fund" published_on = "Friday, 19th May 2006, 06:00 pm" -solved_by = 10074 +solved_by = 10101 difficulty_rating = "35%" content = """ A bag contains one red disc and one blue disc. In a game of chance a player takes a disc at random and its colour is noted. diff --git a/src/P122/problem.jl b/src/P122/problem.jl index 47a20fa..10e2da0 100644 --- a/src/P122/problem.jl +++ b/src/P122/problem.jl @@ -3,7 +3,7 @@ module Problem122 title = "Problem 122: Efficient exponentiation" published_on = "Friday, 2nd June 2006, 06:00 pm" -solved_by = 8112 +solved_by = 8142 difficulty_rating = "40%" content = """ The most naive way of computing n¹⁵ requires fourteen multiplications: diff --git a/src/P123/problem.jl b/src/P123/problem.jl index 9f2dc93..e7b6dd3 100644 --- a/src/P123/problem.jl +++ b/src/P123/problem.jl @@ -3,7 +3,7 @@ module Problem123 title = "Problem 123: Prime square remainders" published_on = "Friday, 16th June 2006, 06:00 pm" -solved_by = 11937 +solved_by = 11971 difficulty_rating = "30%" content = """ Let pⁿ be the nth prime: 2, 3, 5, 7, 11, ..., and let r be the remainder when (pₙ-1)ⁿ + (pₙ+1)ⁿ is divided by pₙ². diff --git a/src/P124/problem.jl b/src/P124/problem.jl index 60a4706..06ae411 100644 --- a/src/P124/problem.jl +++ b/src/P124/problem.jl @@ -3,7 +3,7 @@ module Problem124 title = "Problem 124: Ordered radicals" published_on = "Friday, 14th July 2006, 06:00 pm" -solved_by = 14184 +solved_by = 14215 difficulty_rating = "25%" content = """ The radical of n, rad(n), is the product of the distinct prime factors of n. For example, 504 = 2³ × 3² × 7, so rad(504) = 2 × 3 × 7 diff --git a/src/P125/problem.jl b/src/P125/problem.jl index 9c29556..ca77002 100644 --- a/src/P125/problem.jl +++ b/src/P125/problem.jl @@ -3,7 +3,7 @@ module Problem125 title = "Problem 125: Palindromic sums" published_on = "Friday, 4th August 2006, 06:00 pm" -solved_by = 14005 +solved_by = 14044 difficulty_rating = "25%" content = """ The palindromic number 595 is interesting because it can be written as the sum of consecutive squares: 6² + 7² + 8² + 9² + diff --git a/src/P126/problem.jl b/src/P126/problem.jl index b48b5a4..9a6eaf0 100644 --- a/src/P126/problem.jl +++ b/src/P126/problem.jl @@ -3,7 +3,7 @@ module Problem126 title = "Problem 126: Cuboid layers" published_on = "Friday, 18th August 2006, 06:00 pm" -solved_by = 4929 +solved_by = 4946 difficulty_rating = "55%" content = """ The minimum number of cubes to cover every visible face on a cuboid measuring 3 x 2 x 1 is twenty-two. diff --git a/src/P127/problem.jl b/src/P127/problem.jl index 5375538..a2494fa 100644 --- a/src/P127/problem.jl +++ b/src/P127/problem.jl @@ -3,7 +3,7 @@ module Problem127 title = "Problem 127: abc-hits" published_on = "Friday, 1st September 2006, 06:00 pm" -solved_by = 6478 +solved_by = 6499 difficulty_rating = "50%" content = """ The radical of n, rad(n), is the product of distinct prime factors of n. For example, 504 = 2³ × 3² × 7, so rad(504) = 2 × 3 × 7 diff --git a/src/P128/problem.jl b/src/P128/problem.jl index bb76b9a..5d412ac 100644 --- a/src/P128/problem.jl +++ b/src/P128/problem.jl @@ -3,7 +3,7 @@ module Problem128 title = "Problem 128: Hexagonal tile differences" published_on = "Friday, 29th September 2006, 06:00 pm" -solved_by = 5214 +solved_by = 5226 difficulty_rating = "55%" content = """ A hexagonal tile with number 1 is surrounded by a ring of six hexagonal tiles, starting at "12 o'clock" and numbering the tiles 2 to 7 in an anti-clockwise direction. diff --git a/src/P129/problem.jl b/src/P129/problem.jl index ae8a1f5..f171d66 100644 --- a/src/P129/problem.jl +++ b/src/P129/problem.jl @@ -3,7 +3,7 @@ module Problem129 title = "Problem 129: Repunit divisibility" published_on = "Friday, 27th October 2006, 06:00 pm" -solved_by = 6522 +solved_by = 6543 difficulty_rating = "45%" content = """ A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k; for example, R(6) = diff --git a/src/P13/problem.jl b/src/P13/problem.jl index 0a7da41..844ee65 100644 --- a/src/P13/problem.jl +++ b/src/P13/problem.jl @@ -3,7 +3,7 @@ module Problem13 title = "Problem 13: Large sum" published_on = "Friday, 22nd March 2002, 06:00 pm" -solved_by = 232497 +solved_by = 232713 difficulty_rating = "5%" content = """ Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. diff --git a/src/P130/problem.jl b/src/P130/problem.jl index 75cf87b..0dc4a1d 100644 --- a/src/P130/problem.jl +++ b/src/P130/problem.jl @@ -3,7 +3,7 @@ module Problem130 title = "Problem 130: Composites with prime repunit property" published_on = "Friday, 27th October 2006, 06:00 pm" -solved_by = 6142 +solved_by = 6165 difficulty_rating = "45%" content = """ A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k; for example, R(6) = diff --git a/src/P131/problem.jl b/src/P131/problem.jl index c6c4556..f37b031 100644 --- a/src/P131/problem.jl +++ b/src/P131/problem.jl @@ -3,7 +3,7 @@ module Problem131 title = "Problem 131: Prime cube partnership" published_on = "Friday, 10th November 2006, 06:00 pm" -solved_by = 7614 +solved_by = 7652 difficulty_rating = "40%" content = """ There are some prime values, p, for which there exists a positive integer, n, such that the expression n³ + n²p is a perfect cube. diff --git a/src/P132/problem.jl b/src/P132/problem.jl index e976465..2c6a19c 100644 --- a/src/P132/problem.jl +++ b/src/P132/problem.jl @@ -3,7 +3,7 @@ module Problem132 title = "Problem 132: Large repunit factors" published_on = "Friday, 1st December 2006, 06:00 pm" -solved_by = 6566 +solved_by = 6593 difficulty_rating = "45%" content = """ A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k. diff --git a/src/P133/problem.jl b/src/P133/problem.jl index 6888273..bce90c0 100644 --- a/src/P133/problem.jl +++ b/src/P133/problem.jl @@ -3,7 +3,7 @@ module Problem133 title = "Problem 133: Repunit nonfactors" published_on = "Friday, 1st December 2006, 06:00 pm" -solved_by = 5731 +solved_by = 5752 difficulty_rating = "50%" content = """ A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k; for example, R(6) = diff --git a/src/P134/problem.jl b/src/P134/problem.jl index dd71b1d..8f7d884 100644 --- a/src/P134/problem.jl +++ b/src/P134/problem.jl @@ -3,7 +3,7 @@ module Problem134 title = "Problem 134: Prime pair connection" published_on = "Friday, 15th December 2006, 06:00 pm" -solved_by = 7254 +solved_by = 7277 difficulty_rating = "45%" content = """ Consider the consecutive primes p₁ = 19 and p₂ = 23. It can be verified that 1219 is the smallest number such that the last diff --git a/src/P135/problem.jl b/src/P135/problem.jl index db9db6b..595fee5 100644 --- a/src/P135/problem.jl +++ b/src/P135/problem.jl @@ -3,7 +3,7 @@ module Problem135 title = "Problem 135: Same differences" published_on = "Friday, 29th December 2006, 06:00 pm" -solved_by = 6614 +solved_by = 6638 difficulty_rating = "45%" content = """ Given the positive integers, x, y, and z, are consecutive terms of an arithmetic progression, the least value of the positive diff --git a/src/P136/problem.jl b/src/P136/problem.jl index a4169b6..a46aa6e 100644 --- a/src/P136/problem.jl +++ b/src/P136/problem.jl @@ -3,7 +3,7 @@ module Problem136 title = "Problem 136: Singleton difference" published_on = "Friday, 29th December 2006, 06:00 pm" -solved_by = 5884 +solved_by = 5906 difficulty_rating = "50%" content = """ The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. Given that n is a positive integer, the diff --git a/src/P137/problem.jl b/src/P137/problem.jl index dfa9da6..7d6f400 100644 --- a/src/P137/problem.jl +++ b/src/P137/problem.jl @@ -3,7 +3,7 @@ module Problem137 title = "Problem 137: Fibonacci golden nuggets" published_on = "Friday, 12th January 2007, 06:00 pm" -solved_by = 5717 +solved_by = 5739 difficulty_rating = "50%" content = """ Consider the infinite polynomial series A_F(x) = x F_1 + x^2 F_2 + x^3 F_3 + \\dots, where F_k is the kth term in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, \\dots; that is, F_k = F_{k-1} + F_{k-2}, F_1 = 1 and F_2 = 1. diff --git a/src/P138/problem.jl b/src/P138/problem.jl index 41c89b0..abf5679 100644 --- a/src/P138/problem.jl +++ b/src/P138/problem.jl @@ -3,7 +3,7 @@ module Problem138 title = "Problem 138: Special isosceles triangles" published_on = "Saturday, 20th January 2007, 11:00 am" -solved_by = 6029 +solved_by = 6054 difficulty_rating = "45%" content = """ Consider the isosceles triangle with base length, b = 16, and legs, L = 17. diff --git a/src/P139/problem.jl b/src/P139/problem.jl index 60594f8..bdc59af 100644 --- a/src/P139/problem.jl +++ b/src/P139/problem.jl @@ -3,7 +3,7 @@ module Problem139 title = "Problem 139: Pythagorean tiles" published_on = "Saturday, 27th January 2007, 09:00 am" -solved_by = 5841 +solved_by = 5865 difficulty_rating = "50%" content = """ Let (a, b, c) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such diff --git a/src/P14/problem.jl b/src/P14/problem.jl index 4fd49fd..de9ba92 100644 --- a/src/P14/problem.jl +++ b/src/P14/problem.jl @@ -3,7 +3,7 @@ module Problem14 title = "Problem 14: Longest Collatz sequence" published_on = "Friday, 5th April 2002, 06:00 pm" -solved_by = 232764 +solved_by = 232970 difficulty_rating = "5%" content = """ The following iterative sequence is defined for the set of positive integers: diff --git a/src/P140/problem.jl b/src/P140/problem.jl index 4d08325..f1f2ab0 100644 --- a/src/P140/problem.jl +++ b/src/P140/problem.jl @@ -3,7 +3,7 @@ module Problem140 title = "Problem 140: Modified Fibonacci golden nuggets" published_on = "Saturday, 3rd February 2007, 07:00 am" -solved_by = 4493 +solved_by = 4518 difficulty_rating = "55%" content = """ Consider the infinite polynomial series A_G(x) = x G_1 + x^2 G_2 + x^3 G_3 + \\cdots, where G_k is the kth term of the second order recurrence relation G_k = G_{k-1} + G_{k-2}, G_1 = 1 and G_2 = 4; that is, 1, 4, 5, 9, 14, 23, \\dots . diff --git a/src/P141/problem.jl b/src/P141/problem.jl index 42d4510..5045a2e 100644 --- a/src/P141/problem.jl +++ b/src/P141/problem.jl @@ -3,7 +3,7 @@ module Problem141 title = "Problem 141: Investigating progressive numbers, n, which are also square" published_on = "Saturday, 17th February 2007, 05:00 am" -solved_by = 4085 +solved_by = 4106 difficulty_rating = "60%" content = """ A positive integer, n, is divided by d and the quotient and remainder are q and r respectively. In addition d, q, and r are diff --git a/src/P142/problem.jl b/src/P142/problem.jl index c0c8d1c..8abf1a1 100644 --- a/src/P142/problem.jl +++ b/src/P142/problem.jl @@ -3,7 +3,7 @@ module Problem142 title = "Problem 142: Perfect Square Collection" published_on = "Saturday, 24th February 2007, 01:00 am" -solved_by = 6011 +solved_by = 6030 difficulty_rating = "45%" content = """ Find the smallest x + y + z with integers x > y > z > 0 such that x + y, x - y, x + z, x - z, y + z, y - z are all perfect squares. diff --git a/src/P143/problem.jl b/src/P143/problem.jl index e9ed612..fede62e 100644 --- a/src/P143/problem.jl +++ b/src/P143/problem.jl @@ -3,7 +3,7 @@ module Problem143 title = "Problem 143: Investigating the Torricelli point of a triangle" published_on = "Friday, 2nd March 2007, 09:00 pm" -solved_by = 2853 +solved_by = 2864 difficulty_rating = "65%" content = """ Let ABC be a triangle with all interior angles being less than 120 degrees. Let X be any point inside the triangle and let XA = p, XC = q, and XB = r. diff --git a/src/P144/problem.jl b/src/P144/problem.jl index 41f0a19..85eca84 100644 --- a/src/P144/problem.jl +++ b/src/P144/problem.jl @@ -3,7 +3,7 @@ module Problem144 title = "Problem 144: Investigating multiple reflections of a laser beam" published_on = "Friday, 9th March 2007, 05:00 pm" -solved_by = 6473 +solved_by = 6494 difficulty_rating = "50%" content = """ In laser physics, a "white cell" is a mirror system that acts as a delay line for the laser beam. The beam enters the cell, bounces around on the mirrors, and eventually works its way back out. diff --git a/src/P145/problem.jl b/src/P145/problem.jl index cc89e2c..fd040e3 100644 --- a/src/P145/problem.jl +++ b/src/P145/problem.jl @@ -3,7 +3,7 @@ module Problem145 title = "Problem 145: How many reversible numbers are there below one-billion?" published_on = "Friday, 16th March 2007, 01:00 pm" -solved_by = 17194 +solved_by = 17243 difficulty_rating = "20%" content = """ Some positive integers n have the property that the sum [ n + reverse(n) ] consists entirely of odd (decimal) digits. For instance, diff --git a/src/P146/problem.jl b/src/P146/problem.jl index 896aa28..7148773 100644 --- a/src/P146/problem.jl +++ b/src/P146/problem.jl @@ -3,7 +3,7 @@ module Problem146 title = "Problem 146: Investigating a Prime Pattern" published_on = "Saturday, 24th March 2007, 09:00 am" -solved_by = 5238 +solved_by = 5258 difficulty_rating = "50%" content = """ The smallest positive integer n for which the numbers n²+1, n²+3, n²+7, n²+9, n²+13, and n²+27 are consecutive primes is 10. diff --git a/src/P147/problem.jl b/src/P147/problem.jl index 8dd6fba..72c881a 100644 --- a/src/P147/problem.jl +++ b/src/P147/problem.jl @@ -3,7 +3,7 @@ module Problem147 title = "Problem 147: Rectangles in cross-hatched grids" published_on = "Saturday, 31st March 2007, 06:00 am" -solved_by = 3140 +solved_by = 3149 difficulty_rating = "65%" content = """ In a 3x2 cross-hatched grid, a total of 37 different rectangles could be situated within that grid as indicated in the sketch. diff --git a/src/P148/problem.jl b/src/P148/problem.jl index 306e616..99b06b1 100644 --- a/src/P148/problem.jl +++ b/src/P148/problem.jl @@ -3,7 +3,7 @@ module Problem148 title = "Problem 148: Exploring Pascal's triangle" published_on = "Saturday, 7th April 2007, 02:00 am" -solved_by = 5306 +solved_by = 5334 difficulty_rating = "50%" content = """ We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by 7: diff --git a/src/P149/problem.jl b/src/P149/problem.jl index 60de4ad..b9fa4ce 100644 --- a/src/P149/problem.jl +++ b/src/P149/problem.jl @@ -3,7 +3,7 @@ module Problem149 title = "Problem 149: Searching for a maximum-sum subsequence" published_on = "Friday, 13th April 2007, 10:00 pm" -solved_by = 4988 +solved_by = 5008 difficulty_rating = "50%" content = """ Looking at the table below, it is easy to verify that the maximum possible sum of adjacent numbers in any direction (horizontal, diff --git a/src/P15/problem.jl b/src/P15/problem.jl index 36c1d82..b3b3a00 100644 --- a/src/P15/problem.jl +++ b/src/P15/problem.jl @@ -3,7 +3,7 @@ module Problem15 title = "Problem 15: Lattice paths" published_on = "Friday, 19th April 2002, 06:00 pm" -solved_by = 192357 +solved_by = 192534 difficulty_rating = "5%" content = """ Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the diff --git a/src/P150/problem.jl b/src/P150/problem.jl index 5980700..02ffa7a 100644 --- a/src/P150/problem.jl +++ b/src/P150/problem.jl @@ -3,7 +3,7 @@ module Problem150 title = "Problem 150: Searching a triangular array for a sub-triangle having minimum-sum" published_on = "Friday, 13th April 2007, 10:00 pm" -solved_by = 4074 +solved_by = 4093 difficulty_rating = "55%" content = """ In a triangular array of positive and negative integers, we wish to find a sub-triangle such that the sum of the numbers it contains is the smallest possible. diff --git a/src/P151/problem.jl b/src/P151/problem.jl index 0be9bf0..d7a2e45 100644 --- a/src/P151/problem.jl +++ b/src/P151/problem.jl @@ -3,7 +3,7 @@ module Problem151 title = "Problem 151: Paper sheets of standard sizes: an expected-value problem" published_on = "Friday, 20th April 2007, 06:00 pm" -solved_by = 5690 +solved_by = 5715 difficulty_rating = "50%" content = """ A printing shop runs 16 batches (jobs) every week and each batch requires a sheet of special colour-proofing paper of size A5. diff --git a/src/P152/problem.jl b/src/P152/problem.jl index 3d548b8..2ee42c2 100644 --- a/src/P152/problem.jl +++ b/src/P152/problem.jl @@ -3,7 +3,7 @@ module Problem152 title = "Problem 152: Writing 1/2 as a sum of inverse squares" published_on = "Friday, 27th April 2007, 02:00 pm" -solved_by = 2766 +solved_by = 2785 difficulty_rating = "65%" content = """ There are several ways to write the number 1/2 as a sum of inverse squares using diff --git a/src/P153/problem.jl b/src/P153/problem.jl index dbffa2b..b93616f 100644 --- a/src/P153/problem.jl +++ b/src/P153/problem.jl @@ -3,7 +3,7 @@ module Problem153 title = "Problem 153: Investigating Gaussian Integers" published_on = "Saturday, 5th May 2007, 10:00 am" -solved_by = 2700 +solved_by = 2713 difficulty_rating = "65%" content = """ As we all know the equation diff --git a/src/P154/problem.jl b/src/P154/problem.jl index 0ddb7b0..a8a4ec6 100644 --- a/src/P154/problem.jl +++ b/src/P154/problem.jl @@ -3,7 +3,7 @@ module Problem154 title = "Problem 154: Exploring Pascal's pyramid" published_on = "Saturday, 12th May 2007, 06:00 am" -solved_by = 2712 +solved_by = 2725 difficulty_rating = "65%" content = """ A triangular pyramid is constructed using spherical balls so that each ball rests on exactly three balls of the next lower level. diff --git a/src/P155/problem.jl b/src/P155/problem.jl index 3885149..337ff1a 100644 --- a/src/P155/problem.jl +++ b/src/P155/problem.jl @@ -3,7 +3,7 @@ module Problem155 title = "Problem 155: Counting Capacitor Circuits" published_on = "Saturday, 19th May 2007, 02:00 am" -solved_by = 3710 +solved_by = 3727 difficulty_rating = "60%" content = """ An electric circuit uses exclusively identical capacitors of the same value C. diff --git a/src/P156/problem.jl b/src/P156/problem.jl index 34291e1..0b65fc8 100644 --- a/src/P156/problem.jl +++ b/src/P156/problem.jl @@ -3,7 +3,7 @@ module Problem156 title = "Problem 156: Counting Digits" published_on = "Friday, 25th May 2007, 10:00 pm" -solved_by = 2510 +solved_by = 2519 difficulty_rating = "70%" content = """ Starting from zero the natural numbers are written down in base 10 like this: diff --git a/src/P157/problem.jl b/src/P157/problem.jl index 432ae5e..ef93c4c 100644 --- a/src/P157/problem.jl +++ b/src/P157/problem.jl @@ -3,7 +3,7 @@ module Problem157 title = "Problem 157: Solving the diophantine equation ¹/a + ¹/b = ᵖ/₁₀ⁿ" published_on = "Friday, 1st June 2007, 06:00 pm" -solved_by = 2808 +solved_by = 2823 difficulty_rating = "65%" content = """ Consider the diophantine equation ¹/a + ¹/b = ᵖ/₁₀ⁿ with a, b, p, n positive integers and a ≤ b. diff --git a/src/P158/problem.jl b/src/P158/problem.jl index 8e7866f..09ca4c4 100644 --- a/src/P158/problem.jl +++ b/src/P158/problem.jl @@ -3,7 +3,7 @@ module Problem158 title = "Problem 158: Exploring strings for which only one character comes lexicographically after its neighbour to the left" published_on = "Friday, 15th June 2007, 02:00 pm" -solved_by = 3742 +solved_by = 3753 difficulty_rating = "55%" content = """ Taking three different letters from the 26 letters of the alphabet, character strings of length three can be formed. diff --git a/src/P159/problem.jl b/src/P159/problem.jl index a423a29..6dd5987 100644 --- a/src/P159/problem.jl +++ b/src/P159/problem.jl @@ -3,7 +3,7 @@ module Problem159 title = "Problem 159: Digital root sums of factorisations" published_on = "Saturday, 30th June 2007, 02:00 pm" -solved_by = 3394 +solved_by = 3409 difficulty_rating = "60%" content = """ A composite number can be factored many different ways. For instance, not including multiplication by one, 24 can be factored diff --git a/src/P16/problem.jl b/src/P16/problem.jl index 3d398dd..75feae2 100644 --- a/src/P16/problem.jl +++ b/src/P16/problem.jl @@ -3,7 +3,7 @@ module Problem16 title = "Problem 16: Power digit sum" published_on = "Friday, 3rd May 2002, 06:00 pm" -solved_by = 234981 +solved_by = 235183 difficulty_rating = "5%" content = """ 2¹⁵ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. diff --git a/src/P160/problem.jl b/src/P160/problem.jl index a8edf42..add74bd 100644 --- a/src/P160/problem.jl +++ b/src/P160/problem.jl @@ -3,7 +3,7 @@ module Problem160 title = "Problem 160: Factorial trailing digits" published_on = "Friday, 7th September 2007, 02:00 pm" -solved_by = 3611 +solved_by = 3627 difficulty_rating = "60%" content = """ For any N, let f(N) be the last five digits before the trailing zeroes in N!. diff --git a/src/P161/problem.jl b/src/P161/problem.jl index e9d5928..fc729f4 100644 --- a/src/P161/problem.jl +++ b/src/P161/problem.jl @@ -3,7 +3,7 @@ module Problem161 title = "Problem 161: Triominoes" published_on = "Friday, 21st September 2007, 06:00 pm" -solved_by = 2195 +solved_by = 2207 difficulty_rating = "70%" content = """ A triomino is a shape consisting of three squares joined via the edges. diff --git a/src/P162/problem.jl b/src/P162/problem.jl index 96c2afc..29372d4 100644 --- a/src/P162/problem.jl +++ b/src/P162/problem.jl @@ -3,7 +3,7 @@ module Problem162 title = "Problem 162: Hexadecimal numbers" published_on = "Friday, 5th October 2007, 10:00 pm" -solved_by = 5520 +solved_by = 5528 difficulty_rating = "45%" content = """ In the hexadecimal number system numbers are represented using 16 different digits: diff --git a/src/P163/problem.jl b/src/P163/problem.jl index 43767db..7923b6d 100644 --- a/src/P163/problem.jl +++ b/src/P163/problem.jl @@ -3,7 +3,7 @@ module Problem163 title = "Problem 163: Cross-hatched triangles" published_on = "Saturday, 13th October 2007, 02:00 am" -solved_by = 1877 +solved_by = 1890 difficulty_rating = "70%" content = """ Consider an equilateral triangle in which straight lines are drawn from each vertex to the middle of the opposite side, such as in the diff --git a/src/P164/problem.jl b/src/P164/problem.jl index c53025f..04ea454 100644 --- a/src/P164/problem.jl +++ b/src/P164/problem.jl @@ -3,7 +3,7 @@ module Problem164 title = "Problem 164: Numbers for which no three consecutive digits have a sum greater than a given value" published_on = "Saturday, 20th October 2007, 06:00 am" -solved_by = 5922 +solved_by = 5939 difficulty_rating = "45%" content = """ How many 20 digit numbers n (without any leading zero) exist such that no three consecutive digits of n have a sum greater diff --git a/src/P165/problem.jl b/src/P165/problem.jl index b7d6963..a224767 100644 --- a/src/P165/problem.jl +++ b/src/P165/problem.jl @@ -3,7 +3,7 @@ module Problem165 title = "Problem 165: Intersections" published_on = "Saturday, 27th October 2007, 10:00 am" -solved_by = 2686 +solved_by = 2697 difficulty_rating = "65%" content = """ A segment is uniquely defined by its two endpoints. diff --git a/src/P166/problem.jl b/src/P166/problem.jl index a2a2085..746e55a 100644 --- a/src/P166/problem.jl +++ b/src/P166/problem.jl @@ -3,7 +3,7 @@ module Problem166 title = "Problem 166: Criss Cross" published_on = "Saturday, 3rd November 2007, 01:00 pm" -solved_by = 4238 +solved_by = 4253 difficulty_rating = "50%" content = """ A 4x4 grid is filled with digits d, 0 ≤ d ≤ 9. diff --git a/src/P167/problem.jl b/src/P167/problem.jl index b1895f7..8e8fddd 100644 --- a/src/P167/problem.jl +++ b/src/P167/problem.jl @@ -3,7 +3,7 @@ module Problem167 title = "Problem 167: Investigating Ulam sequences" published_on = "Friday, 9th November 2007, 01:00 pm" -solved_by = 1748 +solved_by = 1756 difficulty_rating = "75%" content = """ For two positive integers a and b, the Ulam sequence U(a,b) is defined by U(a,b)₁ = a, U(a,b)₂ = b and for k > 2, U(a,b)ₖ is the diff --git a/src/P168/problem.jl b/src/P168/problem.jl index 42bfb33..8c4f243 100644 --- a/src/P168/problem.jl +++ b/src/P168/problem.jl @@ -3,7 +3,7 @@ module Problem168 title = "Problem 168: Number Rotations" published_on = "Friday, 16th November 2007, 05:00 pm" -solved_by = 2727 +solved_by = 2746 difficulty_rating = "65%" content = """ Consider the number 142857. We can right-rotate this number by moving the last digit (7) to the front of it, giving us 714285. diff --git a/src/P169/problem.jl b/src/P169/problem.jl index 0157e0c..8285355 100644 --- a/src/P169/problem.jl +++ b/src/P169/problem.jl @@ -3,7 +3,7 @@ module Problem169 title = "Problem 169: Exploring the number of different ways a number can be expressed as a sum of powers of 2" published_on = "Friday, 23rd November 2007, 09:00 pm" -solved_by = 5198 +solved_by = 5224 difficulty_rating = "50%" content = """ Define f(0)=1 and f(n) to be the number of different ways n can be expressed as a sum of integer powers of 2 using each power diff --git a/src/P17/problem.jl b/src/P17/problem.jl index aa50798..9a225fa 100644 --- a/src/P17/problem.jl +++ b/src/P17/problem.jl @@ -3,7 +3,7 @@ module Problem17 title = "Problem 17: Number letter counts" published_on = "Friday, 17th May 2002, 06:00 pm" -solved_by = 156350 +solved_by = 156530 difficulty_rating = "5%" content = """ If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in diff --git a/src/P170/problem.jl b/src/P170/problem.jl index 8e898c6..67d152f 100644 --- a/src/P170/problem.jl +++ b/src/P170/problem.jl @@ -3,7 +3,7 @@ module Problem170 title = "Problem 170: Find the largest 0 to 9 pandigital that can be formed by concatenating products" published_on = "Saturday, 1st December 2007, 01:00 am" -solved_by = 2054 +solved_by = 2064 difficulty_rating = "70%" content = """ Take the number 6 and multiply it by each of 1273 and 9854: diff --git a/src/P171/problem.jl b/src/P171/problem.jl index 1dcd252..f11a713 100644 --- a/src/P171/problem.jl +++ b/src/P171/problem.jl @@ -3,7 +3,7 @@ module Problem171 title = "Problem 171: Finding numbers for which the sum of the squares of the digits is a square" published_on = "Saturday, 8th December 2007, 05:00 am" -solved_by = 2862 +solved_by = 2878 difficulty_rating = "65%" content = """ For a positive integer n, let f(n) be the sum of the squares of the digits (in base 10) of n, e.g. diff --git a/src/P172/problem.jl b/src/P172/problem.jl index 9417736..c8b386b 100644 --- a/src/P172/problem.jl +++ b/src/P172/problem.jl @@ -3,7 +3,7 @@ module Problem172 title = "Problem 172: Investigating numbers with few repeated digits" published_on = "Saturday, 15th December 2007, 09:00 am" -solved_by = 3885 +solved_by = 3904 difficulty_rating = "55%" content = """ How many 18-digit numbers n (without leading zeros) are there such that no digit occurs more than three times in n? diff --git a/src/P173/problem.jl b/src/P173/problem.jl index 6790a55..a6b67aa 100644 --- a/src/P173/problem.jl +++ b/src/P173/problem.jl @@ -3,7 +3,7 @@ module Problem173 title = "Problem 173: Using up to one million tiles how many different \"hollow\" square laminae can be formed?" published_on = "Saturday, 22nd December 2007, 01:00 pm" -solved_by = 9320 +solved_by = 9347 difficulty_rating = "30%" content = """ We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal diff --git a/src/P174/problem.jl b/src/P174/problem.jl index 4b93793..12de617 100644 --- a/src/P174/problem.jl +++ b/src/P174/problem.jl @@ -3,7 +3,7 @@ module Problem174 title = "Problem 174: Counting the number of \"hollow\" square laminae that can form one, two, three, ... distinct arrangements" published_on = "Saturday, 22nd December 2007, 01:00 pm" -solved_by = 6007 +solved_by = 6025 difficulty_rating = "40%" content = """ We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal diff --git a/src/P175/problem.jl b/src/P175/problem.jl index abc9ac8..9d9cf80 100644 --- a/src/P175/problem.jl +++ b/src/P175/problem.jl @@ -3,7 +3,7 @@ module Problem175 title = "Problem 175: Fractions involving the number of different ways a number can be expressed as a sum of powers of 2" published_on = "Friday, 28th December 2007, 01:00 pm" -solved_by = 1842 +solved_by = 1847 difficulty_rating = "70%" content = """ Define f(0)=1 and f(n) to be the number of ways to write n as a sum of powers of 2 where no power occurs more than twice. diff --git a/src/P176/problem.jl b/src/P176/problem.jl index 45852d7..ec9416b 100644 --- a/src/P176/problem.jl +++ b/src/P176/problem.jl @@ -3,7 +3,7 @@ module Problem176 title = "Problem 176: Right-angled triangles that share a cathetus" published_on = "Friday, 4th January 2008, 05:00 pm" -solved_by = 1953 +solved_by = 1959 difficulty_rating = "70%" content = """ The four right-angled triangles with sides (9,12,15), (12,16,20), (5,12,13) and (12,35,37) all have one of the shorter sides diff --git a/src/P177/problem.jl b/src/P177/problem.jl index caae122..69cd62f 100644 --- a/src/P177/problem.jl +++ b/src/P177/problem.jl @@ -3,7 +3,7 @@ module Problem177 title = "Problem 177: Integer angled Quadrilaterals" published_on = "Friday, 11th January 2008, 09:00 pm" -solved_by = 1319 +solved_by = 1326 difficulty_rating = "80%" content = """ Let ABCD be a convex quadrilateral, with diagonals AC and BD. At each vertex the diagonal makes an angle with each of the two sides, creating eight corner angles. diff --git a/src/P178/problem.jl b/src/P178/problem.jl index 3d37133..b92f9e1 100644 --- a/src/P178/problem.jl +++ b/src/P178/problem.jl @@ -3,7 +3,7 @@ module Problem178 title = "Problem 178: Step Numbers" published_on = "Saturday, 19th January 2008, 01:00 am" -solved_by = 3503 +solved_by = 3516 difficulty_rating = "55%" content = """ Consider the number 45656. diff --git a/src/P179/problem.jl b/src/P179/problem.jl index 3c9bf15..bfc8b8e 100644 --- a/src/P179/problem.jl +++ b/src/P179/problem.jl @@ -3,7 +3,7 @@ module Problem179 title = "Problem 179: Consecutive positive divisors" published_on = "Saturday, 26th January 2008, 05:00 am" -solved_by = 11529 +solved_by = 11564 difficulty_rating = "25%" content = """ Find the number of integers 1 < n < 10⁷, for which n and n + 1 have the same number of positive divisors. For example, 14 has diff --git a/src/P18/problem.jl b/src/P18/problem.jl index 54f5d53..94acb87 100644 --- a/src/P18/problem.jl +++ b/src/P18/problem.jl @@ -3,7 +3,7 @@ module Problem18 title = "Problem 18: Maximum path sum I" published_on = "Friday, 31st May 2002, 06:00 pm" -solved_by = 149703 +solved_by = 149874 difficulty_rating = "5%" content = """ By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to diff --git a/src/P180/problem.jl b/src/P180/problem.jl index 7426827..809d821 100644 --- a/src/P180/problem.jl +++ b/src/P180/problem.jl @@ -3,7 +3,7 @@ module Problem180 title = "Problem 180: Rational zeros of a function of three variables" published_on = "Saturday, 2nd February 2008, 09:00 am" -solved_by = 1624 +solved_by = 1631 difficulty_rating = "75%" content = """ For any integer n, consider the three functions diff --git a/src/P181/problem.jl b/src/P181/problem.jl index 654daeb..6afe7b2 100644 --- a/src/P181/problem.jl +++ b/src/P181/problem.jl @@ -3,7 +3,7 @@ module Problem181 title = "Problem 181: Investigating in how many ways objects of two different colours can be grouped" published_on = "Saturday, 9th February 2008, 01:00 pm" -solved_by = 2040 +solved_by = 2054 difficulty_rating = "70%" content = """ Having three black objects B and one white object W they can be grouped in 7 ways like this: diff --git a/src/P182/problem.jl b/src/P182/problem.jl index dc187b2..ffd1335 100644 --- a/src/P182/problem.jl +++ b/src/P182/problem.jl @@ -3,7 +3,7 @@ module Problem182 title = "Problem 182: RSA encryption" published_on = "Friday, 15th February 2008, 01:00 pm" -solved_by = 2672 +solved_by = 2676 difficulty_rating = "60%" content = """ The RSA encryption is based on the following procedure: diff --git a/src/P183/problem.jl b/src/P183/problem.jl index d497b90..30c99aa 100644 --- a/src/P183/problem.jl +++ b/src/P183/problem.jl @@ -3,7 +3,7 @@ module Problem183 title = "Problem 183: Maximum product of parts" published_on = "Friday, 22nd February 2008, 05:00 pm" -solved_by = 4791 +solved_by = 4809 difficulty_rating = "45%" content = """ Let N be a positive integer and let N be split into k equal parts, r = N/k, so that N = r + r + ... + r. diff --git a/src/P184/problem.jl b/src/P184/problem.jl index f8f584e..9b65d36 100644 --- a/src/P184/problem.jl +++ b/src/P184/problem.jl @@ -3,7 +3,7 @@ module Problem184 title = "Problem 184: Triangles containing the origin" published_on = "Friday, 29th February 2008, 09:00 pm" -solved_by = 1696 +solved_by = 1702 difficulty_rating = "75%" content = """ Consider the set diff --git a/src/P185/problem.jl b/src/P185/problem.jl index 2ebba63..d327752 100644 --- a/src/P185/problem.jl +++ b/src/P185/problem.jl @@ -3,7 +3,7 @@ module Problem185 title = "Problem 185: Number Mind" published_on = "Saturday, 8th March 2008, 01:00 am" -solved_by = 3212 +solved_by = 3225 difficulty_rating = "55%" content = """ The game Number Mind is a variant of the well known game Master Mind. diff --git a/src/P186/problem.jl b/src/P186/problem.jl index c6ee6d4..d8a4b43 100644 --- a/src/P186/problem.jl +++ b/src/P186/problem.jl @@ -3,7 +3,7 @@ module Problem186 title = "Problem 186: Connectedness of a network" published_on = "Saturday, 15th March 2008, 05:00 am" -solved_by = 2942 +solved_by = 2959 difficulty_rating = "60%" content = """ Here are the records from a busy telephone system with one million users: diff --git a/src/P187/problem.jl b/src/P187/problem.jl index 4119dd0..1237633 100644 --- a/src/P187/problem.jl +++ b/src/P187/problem.jl @@ -3,7 +3,7 @@ module Problem187 title = "Problem 187: Semiprimes" published_on = "Saturday, 22nd March 2008, 09:00 am" -solved_by = 11446 +solved_by = 11472 difficulty_rating = "25%" content = """ A composite is a number containing at least two prime factors. For example, 15 = 3 × 5; 9 = 3 × 3; 12 = 2 × 2 × 3. diff --git a/src/P188/problem.jl b/src/P188/problem.jl index 0d532ff..91e3bec 100644 --- a/src/P188/problem.jl +++ b/src/P188/problem.jl @@ -3,7 +3,7 @@ module Problem188 title = "Problem 188: The hyperexponentiation of a number" published_on = "Friday, 4th April 2008, 02:00 pm" -solved_by = 6522 +solved_by = 6543 difficulty_rating = "35%" content = """ The hyperexponentiation or tetration of a number a by a positive integer b, denoted by a↑↑b or bᵃ, is recursively defined by: diff --git a/src/P189/problem.jl b/src/P189/problem.jl index c2510a5..50dabef 100644 --- a/src/P189/problem.jl +++ b/src/P189/problem.jl @@ -3,7 +3,7 @@ module Problem189 title = "Problem 189: Tri-colouring a triangular grid" published_on = "Friday, 11th April 2008, 05:00 pm" -solved_by = 2113 +solved_by = 2121 difficulty_rating = "70%" content = """ Consider the following configuration of 64 triangles: diff --git a/src/P19/problem.jl b/src/P19/problem.jl index bdd9419..2e75018 100644 --- a/src/P19/problem.jl +++ b/src/P19/problem.jl @@ -3,7 +3,7 @@ module Problem19 title = "Problem 19: Counting Sundays" published_on = "Friday, 14th June 2002, 06:00 pm" -solved_by = 139104 +solved_by = 139267 difficulty_rating = "5%" content = """ You are given the following information, but you may prefer to do some research for yourself. diff --git a/src/P190/problem.jl b/src/P190/problem.jl index e876883..68e6be1 100644 --- a/src/P190/problem.jl +++ b/src/P190/problem.jl @@ -3,7 +3,7 @@ module Problem190 title = "Problem 190: Maximising a weighted product" published_on = "Friday, 18th April 2008, 10:00 pm" -solved_by = 4262 +solved_by = 4276 difficulty_rating = "50%" content = """ Let Sₘ = (x₁, x₂, ... , xₘ) be the m-tuple of positive real numbers with x₁ + x₂ + ... + xₘ = m for which Pₘ = x₁ * x₂² * ... * xₘᵐ is diff --git a/src/P191/problem.jl b/src/P191/problem.jl index 489c7d1..22a4732 100644 --- a/src/P191/problem.jl +++ b/src/P191/problem.jl @@ -3,7 +3,7 @@ module Problem191 title = "Problem 191: Prize Strings" published_on = "Saturday, 26th April 2008, 01:00 am" -solved_by = 7259 +solved_by = 7279 difficulty_rating = "35%" content = """ A particular school offers cash rewards to children with good attendance and punctuality. If they are absent for three diff --git a/src/P192/problem.jl b/src/P192/problem.jl index 8c46c9e..d9240d2 100644 --- a/src/P192/problem.jl +++ b/src/P192/problem.jl @@ -3,7 +3,7 @@ module Problem192 title = "Problem 192: Best Approximations" published_on = "Saturday, 3rd May 2008, 05:00 am" -solved_by = 1673 +solved_by = 1683 difficulty_rating = "75%" content = """ Let x be a real number. diff --git a/src/P193/problem.jl b/src/P193/problem.jl index f036146..af30ac9 100644 --- a/src/P193/problem.jl +++ b/src/P193/problem.jl @@ -3,7 +3,7 @@ module Problem193 title = "Problem 193: Squarefree Numbers" published_on = "Saturday, 10th May 2008, 01:00 pm" -solved_by = 3452 +solved_by = 3465 difficulty_rating = "55%" content = """ A positive integer n is called squarefree, if no square of a prime divides n, thus 1, 2, 3, 5, 6, 7, 10, 11 are squarefree, but not 4, diff --git a/src/P194/problem.jl b/src/P194/problem.jl index 2a9ff37..b26c2f5 100644 --- a/src/P194/problem.jl +++ b/src/P194/problem.jl @@ -3,7 +3,7 @@ module Problem194 title = "Problem 194: Coloured Configurations" published_on = "Saturday, 17th May 2008, 10:00 am" -solved_by = 1446 +solved_by = 1452 difficulty_rating = "75%" content = """ Consider graphs built with the units A: diff --git a/src/P195/problem.jl b/src/P195/problem.jl index 9305896..92fc882 100644 --- a/src/P195/problem.jl +++ b/src/P195/problem.jl @@ -3,7 +3,7 @@ module Problem195 title = "Problem 195: Inscribed circles of triangles with one angle of 60 degrees" published_on = "Friday, 23rd May 2008, 02:00 pm" -solved_by = 1432 +solved_by = 1437 difficulty_rating = "75%" content = """ Let's call an integer sided triangle with exactly one angle of 60 degrees a 60-degree triangle. diff --git a/src/P196/problem.jl b/src/P196/problem.jl index da05d2d..fba7ad9 100644 --- a/src/P196/problem.jl +++ b/src/P196/problem.jl @@ -3,7 +3,7 @@ module Problem196 title = "Problem 196: Prime triplets" published_on = "Friday, 30th May 2008, 06:00 pm" -solved_by = 2653 +solved_by = 2661 difficulty_rating = "65%" content = """ Build a triangle from all positive integers in the following way: diff --git a/src/P197/problem.jl b/src/P197/problem.jl index d42e605..32dfc00 100644 --- a/src/P197/problem.jl +++ b/src/P197/problem.jl @@ -3,7 +3,7 @@ module Problem197 title = "Problem 197: Investigating the behaviour of a recursively defined sequence" published_on = "Friday, 6th June 2008, 10:00 pm" -solved_by = 5018 +solved_by = 5030 difficulty_rating = "45%" content = """ Given is the function f(x) = ⌊2³⁰.⁴⁰³²⁴³⁷⁸⁴⁻ˣ²⌋ × 10⁻⁹ ( ⌊ ⌋ is the floor-function), diff --git a/src/P198/problem.jl b/src/P198/problem.jl index d884cef..42cc63f 100644 --- a/src/P198/problem.jl +++ b/src/P198/problem.jl @@ -3,7 +3,7 @@ module Problem198 title = "Problem 198: Ambiguous Numbers" published_on = "Saturday, 14th June 2008, 02:00 am" -solved_by = 1154 +solved_by = 1161 difficulty_rating = "80%" content = """ A best approximation to a real number x for the denominator bound d is a rational number \\frac r s (in reduced form) with s \\le d, so that any rational number \\frac p q which is closer to x than \\frac r s has q > d. diff --git a/src/P199/problem.jl b/src/P199/problem.jl index 03e4b8f..342fdbb 100644 --- a/src/P199/problem.jl +++ b/src/P199/problem.jl @@ -3,7 +3,7 @@ module Problem199 title = "Problem 199: Iterative Circle Packing" published_on = "Saturday, 21st June 2008, 06:00 am" -solved_by = 2010 +solved_by = 2015 difficulty_rating = "70%" content = """ Three circles of equal radius are placed inside a larger circle such that each pair of circles is tangent to one another and the inner circles do not overlap. There are four uncovered "gaps" which are to be filled iteratively with more tangent circles. diff --git a/src/P2/problem.jl b/src/P2/problem.jl index c2ce29c..4a0c5f1 100644 --- a/src/P2/problem.jl +++ b/src/P2/problem.jl @@ -3,7 +3,7 @@ module Problem2 title = "Problem 2: Even Fibonacci numbers" published_on = "Friday, 19th October 2001, 06:00 pm" -solved_by = 774328 +solved_by = 774551 difficulty_rating = "5%" content = """ Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 diff --git a/src/P20/problem.jl b/src/P20/problem.jl index 0274e5f..3eb6b71 100644 --- a/src/P20/problem.jl +++ b/src/P20/problem.jl @@ -3,7 +3,7 @@ module Problem20 title = "Problem 20: Factorial digit sum" published_on = "Friday, 21st June 2002, 06:00 pm" -solved_by = 203576 +solved_by = 203753 difficulty_rating = "5%" content = """ n! means n × (n − 1) × ... × 3 × 2 × 1 diff --git a/src/P200/problem.jl b/src/P200/problem.jl index 8654251..ce82cbd 100644 --- a/src/P200/problem.jl +++ b/src/P200/problem.jl @@ -3,7 +3,7 @@ module Problem200 title = "Problem 200: Find the 200th prime-proof sqube containing the contiguous sub-string \"200\"" published_on = "Saturday, 28th June 2008, 10:00 am" -solved_by = 2437 +solved_by = 2448 difficulty_rating = "65%" content = """ We shall define a sqube to be a number of the form, p²q³, where p and q are distinct primes. diff --git a/src/P201/problem.jl b/src/P201/problem.jl index 7bdb89e..98583b8 100644 --- a/src/P201/problem.jl +++ b/src/P201/problem.jl @@ -3,7 +3,7 @@ module Problem201 title = "Problem 201: Subsets with a unique sum" published_on = "Saturday, 5th July 2008, 02:00 pm" -solved_by = 2374 +solved_by = 2378 difficulty_rating = "65%" content = """ For any set A of numbers, let sum(A) be the sum of the elements of A. diff --git a/src/P202/problem.jl b/src/P202/problem.jl index 393c52f..c19e3e1 100644 --- a/src/P202/problem.jl +++ b/src/P202/problem.jl @@ -3,7 +3,7 @@ module Problem202 title = "Problem 202: Laserbeam" published_on = "Saturday, 5th July 2008, 02:00 pm" -solved_by = 2625 +solved_by = 2633 difficulty_rating = "60%" content = """ Three mirrors are arranged in the shape of an equilateral triangle, with their reflective surfaces pointing inwards. There is an infinitesimal gap at each vertex of the triangle through which a laser beam may pass. diff --git a/src/P203/problem.jl b/src/P203/problem.jl index efa5c35..346e581 100644 --- a/src/P203/problem.jl +++ b/src/P203/problem.jl @@ -3,7 +3,7 @@ module Problem203 title = "Problem 203: Squarefree Binomial Coefficients" published_on = "Saturday, 6th September 2008, 02:00 pm" -solved_by = 9350 +solved_by = 9374 difficulty_rating = "25%" content = """ The binomial coefficients \\displaystyle \\binom n k can be arranged in triangular form, Pascal's triangle, like this: diff --git a/src/P204/problem.jl b/src/P204/problem.jl index 588dceb..6c0c882 100644 --- a/src/P204/problem.jl +++ b/src/P204/problem.jl @@ -3,7 +3,7 @@ module Problem204 title = "Problem 204: Generalised Hamming Numbers" published_on = "Saturday, 6th September 2008, 02:00 pm" -solved_by = 7513 +solved_by = 7531 difficulty_rating = "30%" content = """ A Hamming number is a positive number which has no prime factor larger than 5. diff --git a/src/P205/problem.jl b/src/P205/problem.jl index 3be5397..4a1dbe0 100644 --- a/src/P205/problem.jl +++ b/src/P205/problem.jl @@ -3,7 +3,7 @@ module Problem205 title = "Problem 205: Dice Game" published_on = "Saturday, 6th September 2008, 02:00 pm" -solved_by = 15257 +solved_by = 15290 difficulty_rating = "15%" content = """ Peter has nine four-sided (pyramidal) dice, each with faces numbered 1, 2, 3, 4. diff --git a/src/P206/problem.jl b/src/P206/problem.jl index 8c08202..67ce334 100644 --- a/src/P206/problem.jl +++ b/src/P206/problem.jl @@ -3,7 +3,7 @@ module Problem206 title = "Problem 206: Concealed Square" published_on = "Saturday, 6th September 2008, 02:00 pm" -solved_by = 25077 +solved_by = 25118 difficulty_rating = "5%" content = """ Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0, diff --git a/src/P207/problem.jl b/src/P207/problem.jl index d1af289..3a08f64 100644 --- a/src/P207/problem.jl +++ b/src/P207/problem.jl @@ -3,7 +3,7 @@ module Problem207 title = "Problem 207: Integer partition equations" published_on = "Saturday, 6th September 2008, 02:00 pm" -solved_by = 4813 +solved_by = 4821 difficulty_rating = "40%" content = """ For some positive integers k, there exists an integer partition of the form 4ᵗ = 2ᵗ + k, diff --git a/src/P208/problem.jl b/src/P208/problem.jl index 43d09fc..af182b6 100644 --- a/src/P208/problem.jl +++ b/src/P208/problem.jl @@ -3,7 +3,7 @@ module Problem208 title = "Problem 208: Robot Walks" published_on = "Friday, 12th September 2008, 02:00 pm" -solved_by = 1800 +solved_by = 1804 difficulty_rating = "70%" content = """ A robot moves in a series of one-fifth circular arcs (72°), with a free choice of a clockwise or an anticlockwise arc for each step, but no turning on the spot. diff --git a/src/P209/problem.jl b/src/P209/problem.jl index ff4bc55..15248f9 100644 --- a/src/P209/problem.jl +++ b/src/P209/problem.jl @@ -3,7 +3,7 @@ module Problem209 title = "Problem 209: Circular Logic" published_on = "Friday, 19th September 2008, 06:00 pm" -solved_by = 2567 +solved_by = 2577 difficulty_rating = "60%" content = """ A k-input binary truth table is a map from k input bits (binary digits, 0 [false] or 1 [true]) to 1 output bit. For example, the 2-input diff --git a/src/P21/problem.jl b/src/P21/problem.jl index a6cdeab..df2cbd5 100644 --- a/src/P21/problem.jl +++ b/src/P21/problem.jl @@ -3,7 +3,7 @@ module Problem21 title = "Problem 21: Amicable numbers" published_on = "Friday, 5th July 2002, 06:00 pm" -solved_by = 150988 +solved_by = 151163 difficulty_rating = "5%" content = """ Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). diff --git a/src/P210/problem.jl b/src/P210/problem.jl index 68072ba..1eb755a 100644 --- a/src/P210/problem.jl +++ b/src/P210/problem.jl @@ -3,7 +3,7 @@ module Problem210 title = "Problem 210: Obtuse Angled Triangles" published_on = "Friday, 26th September 2008, 10:00 pm" -solved_by = 1753 +solved_by = 1765 difficulty_rating = "70%" content = """ Consider the set S(r) of points (x,y) with integer coordinates satisfying |x| + |y| ≤ r. diff --git a/src/P211/problem.jl b/src/P211/problem.jl index c76d374..f1a31bf 100644 --- a/src/P211/problem.jl +++ b/src/P211/problem.jl @@ -3,7 +3,7 @@ module Problem211 title = "Problem 211: Divisor Square Sum" published_on = "Saturday, 4th October 2008, 02:00 am" -solved_by = 4283 +solved_by = 4300 difficulty_rating = "50%" content = """ For a positive integer n, let σ₂(n) be the sum of the squares of its divisors. For example, diff --git a/src/P212/problem.jl b/src/P212/problem.jl index 5af4e76..b9df9c2 100644 --- a/src/P212/problem.jl +++ b/src/P212/problem.jl @@ -3,7 +3,7 @@ module Problem212 title = "Problem 212: Combined Volume of Cuboids" published_on = "Saturday, 11th October 2008, 06:00 am" -solved_by = 1418 +solved_by = 1423 difficulty_rating = "70%" content = """ An axis-aligned cuboid, specified by parameters { (x₀,y₀,z₀), (dx,dy,dz) }, consists of all points (X,Y,Z) such that x₀ ≤ X ≤ x₀+dx, diff --git a/src/P213/problem.jl b/src/P213/problem.jl index d96c63b..2b6f005 100644 --- a/src/P213/problem.jl +++ b/src/P213/problem.jl @@ -3,7 +3,7 @@ module Problem213 title = "Problem 213: Flea Circus" published_on = "Saturday, 18th October 2008, 10:00 am" -solved_by = 2391 +solved_by = 2401 difficulty_rating = "60%" content = """ A 30×30 grid of squares contains 900 fleas, initially one flea per square. diff --git a/src/P214/problem.jl b/src/P214/problem.jl index 52b6d8a..037706a 100644 --- a/src/P214/problem.jl +++ b/src/P214/problem.jl @@ -3,7 +3,7 @@ module Problem214 title = "Problem 214: Totient Chains" published_on = "Saturday, 25th October 2008, 02:00 pm" -solved_by = 5333 +solved_by = 5345 difficulty_rating = "40%" content = """ Let φ be Euler's totient function, i.e. for a natural number n,φ(n) is the number of k, 1 ≤ k ≤ n, for which gcd(k,n) = 1. diff --git a/src/P215/problem.jl b/src/P215/problem.jl index 9d962c2..68c87f9 100644 --- a/src/P215/problem.jl +++ b/src/P215/problem.jl @@ -3,7 +3,7 @@ module Problem215 title = "Problem 215: Crack-free Walls" published_on = "Friday, 31st October 2008, 01:00 pm" -solved_by = 3779 +solved_by = 3789 difficulty_rating = "50%" content = """ Consider the problem of building a wall out of 2×1 and 3×1 bricks (horizontal×vertical dimensions) such that, for extra strength, diff --git a/src/P216/problem.jl b/src/P216/problem.jl index 2715a38..b8e32a6 100644 --- a/src/P216/problem.jl +++ b/src/P216/problem.jl @@ -3,7 +3,7 @@ module Problem216 title = "Problem 216: Investigating the primality of numbers of the form 2n²-1" published_on = "Friday, 7th November 2008, 05:00 pm" -solved_by = 4169 +solved_by = 4181 difficulty_rating = "45%" content = """ Consider numbers t(n) of the form t(n) = 2n²-1 with n > 1. diff --git a/src/P217/problem.jl b/src/P217/problem.jl index a53fb2b..f7b9c5a 100644 --- a/src/P217/problem.jl +++ b/src/P217/problem.jl @@ -3,7 +3,7 @@ module Problem217 title = "Problem 217: Balanced Numbers" published_on = "Friday, 14th November 2008, 09:00 pm" -solved_by = 1543 +solved_by = 1553 difficulty_rating = "70%" content = """ A positive integer with k (decimal) digits is called balanced if its first ⌈ᵏ/₂⌉ digits sum to the same value as its last ⌈ᵏ/₂⌉ digits, diff --git a/src/P218/problem.jl b/src/P218/problem.jl index f811efc..1bca65c 100644 --- a/src/P218/problem.jl +++ b/src/P218/problem.jl @@ -3,7 +3,7 @@ module Problem218 title = "Problem 218: Perfect right-angled triangles" published_on = "Saturday, 22nd November 2008, 01:00 am" -solved_by = 3097 +solved_by = 3109 difficulty_rating = "55%" content = """ Consider the right angled triangle with sides a=7, b=24 and c=25. The area of this triangle is 84, which is divisible by the perfect diff --git a/src/P219/problem.jl b/src/P219/problem.jl index d0f4865..dac66ea 100644 --- a/src/P219/problem.jl +++ b/src/P219/problem.jl @@ -3,7 +3,7 @@ module Problem219 title = "Problem 219: Skew-cost coding" published_on = "Saturday, 29th November 2008, 05:00 am" -solved_by = 1505 +solved_by = 1510 difficulty_rating = "70%" content = """ Let \e[1mA\e[0m and \e[1mB\e[0m be bit strings (sequences of 0's and 1's). diff --git a/src/P22/problem.jl b/src/P22/problem.jl index bdcad0d..d24d7ca 100644 --- a/src/P22/problem.jl +++ b/src/P22/problem.jl @@ -3,7 +3,7 @@ module Problem22 title = "Problem 22: Names scores" published_on = "Friday, 19th July 2002, 06:00 pm" -solved_by = 138955 +solved_by = 139114 difficulty_rating = "5%" content = """ Using\e[1;35m https://projecteuler.net/project/resources/p022_names.txt \e[0m, a 46K text file containing over five-thousand first names, begin by diff --git a/src/P220/problem.jl b/src/P220/problem.jl index 8bf27bf..90916b6 100644 --- a/src/P220/problem.jl +++ b/src/P220/problem.jl @@ -3,7 +3,7 @@ module Problem220 title = "Problem 220: Heighway Dragon" published_on = "Saturday, 6th December 2008, 09:00 am" -solved_by = 2225 +solved_by = 2236 difficulty_rating = "55%" content = """ Let diff --git a/src/P221/problem.jl b/src/P221/problem.jl index 9c3f043..628755b 100644 --- a/src/P221/problem.jl +++ b/src/P221/problem.jl @@ -3,7 +3,7 @@ module Problem221 title = "Problem 221: Alexandrian Integers" published_on = "Saturday, 13th December 2008, 01:00 pm" -solved_by = 2133 +solved_by = 2140 difficulty_rating = "65%" content = """ We shall call a positive integer diff --git a/src/P222/problem.jl b/src/P222/problem.jl index 9a6b9d7..7d81b62 100644 --- a/src/P222/problem.jl +++ b/src/P222/problem.jl @@ -3,7 +3,7 @@ module Problem222 title = "Problem 222: Sphere Packing" published_on = "Friday, 19th December 2008, 01:00 pm" -solved_by = 2128 +solved_by = 2138 difficulty_rating = "60%" content = """ What is the length of the shortest pipe, of internal radius 50mm, that can fully contain 21 balls of radii 30mm, 31mm, ..., 50mm? diff --git a/src/P223/problem.jl b/src/P223/problem.jl index 030543e..6295c7f 100644 --- a/src/P223/problem.jl +++ b/src/P223/problem.jl @@ -3,7 +3,7 @@ module Problem223 title = "Problem 223: Almost right-angled triangles I" published_on = "Friday, 26th December 2008, 05:00 pm" -solved_by = 1565 +solved_by = 1573 difficulty_rating = "70%" content = """ Let us call an integer sided triangle with sides a ≤ b ≤ c barely acute if the sides satisfy diff --git a/src/P224/problem.jl b/src/P224/problem.jl index 963a049..d603184 100644 --- a/src/P224/problem.jl +++ b/src/P224/problem.jl @@ -3,7 +3,7 @@ module Problem224 title = "Problem 224: Almost right-angled triangles II" published_on = "Friday, 26th December 2008, 05:00 pm" -solved_by = 1262 +solved_by = 1272 difficulty_rating = "75%" content = """ Let us call an integer sided triangle with sides a ≤ b ≤ c barely obtuse if the sides satisfy diff --git a/src/P225/problem.jl b/src/P225/problem.jl index 8d6e2c9..17c8bf6 100644 --- a/src/P225/problem.jl +++ b/src/P225/problem.jl @@ -3,7 +3,7 @@ module Problem225 title = "Problem 225: Tribonacci non-divisors" published_on = "Friday, 26th December 2008, 05:00 pm" -solved_by = 4559 +solved_by = 4571 difficulty_rating = "45%" content = """ diff --git a/src/P226/problem.jl b/src/P226/problem.jl index c83b857..afd2c4c 100644 --- a/src/P226/problem.jl +++ b/src/P226/problem.jl @@ -3,7 +3,7 @@ module Problem226 title = "Problem 226: A Scoop of Blancmange" published_on = "Friday, 2nd January 2009, 09:00 pm" -solved_by = 1784 +solved_by = 1790 difficulty_rating = "65%" content = """ The diff --git a/src/P227/problem.jl b/src/P227/problem.jl index f54fe56..468de5b 100644 --- a/src/P227/problem.jl +++ b/src/P227/problem.jl @@ -3,7 +3,7 @@ module Problem227 title = "Problem 227: The Chase" published_on = "Saturday, 10th January 2009, 01:00 am" -solved_by = 2161 +solved_by = 2166 difficulty_rating = "65%" content = """ The Chase is a game played with two dice and an even number of players. diff --git a/src/P228/problem.jl b/src/P228/problem.jl index 04370ff..72bdeac 100644 --- a/src/P228/problem.jl +++ b/src/P228/problem.jl @@ -3,7 +3,7 @@ module Problem228 title = "Problem 228: Minkowski Sums" published_on = "Saturday, 17th January 2009, 05:00 am" -solved_by = 1361 +solved_by = 1368 difficulty_rating = "70%" content = """ Let diff --git a/src/P229/problem.jl b/src/P229/problem.jl index 12d55ff..36bc442 100644 --- a/src/P229/problem.jl +++ b/src/P229/problem.jl @@ -3,7 +3,7 @@ module Problem229 title = "Problem 229: Four Representations using Squares" published_on = "Saturday, 24th January 2009, 09:00 am" -solved_by = 1509 +solved_by = 1510 difficulty_rating = "70%" content = """ Consider the number 3600. It is very special, because diff --git a/src/P23/problem.jl b/src/P23/problem.jl index 9b6d236..c5f0da7 100644 --- a/src/P23/problem.jl +++ b/src/P23/problem.jl @@ -3,7 +3,7 @@ module Problem23 title = "Problem 23: Non-abundant sums" published_on = "Friday, 2nd August 2002, 06:00 pm" -solved_by = 108084 +solved_by = 108213 difficulty_rating = "5%" content = """ A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of diff --git a/src/P230/problem.jl b/src/P230/problem.jl index c24aacd..40e6eeb 100644 --- a/src/P230/problem.jl +++ b/src/P230/problem.jl @@ -3,7 +3,7 @@ module Problem230 title = "Problem 230: Fibonacci Words" published_on = "Saturday, 31st January 2009, 01:00 pm" -solved_by = 2945 +solved_by = 2963 difficulty_rating = "50%" content = """ For any two strings of digits, A and B, we define F_A,_B to be the sequence (A,B,AB,BAB,ABBAB,...) in which each term is the diff --git a/src/P231/problem.jl b/src/P231/problem.jl index 54f6bf6..7deb9d9 100644 --- a/src/P231/problem.jl +++ b/src/P231/problem.jl @@ -3,7 +3,7 @@ module Problem231 title = "Problem 231: The prime factorisation of binomial coefficients" published_on = "Friday, 6th February 2009, 01:00 pm" -solved_by = 5565 +solved_by = 5581 difficulty_rating = "40%" content = """ The binomial coefficient \\displaystyle \\binom {10} 3 = 120. diff --git a/src/P232/problem.jl b/src/P232/problem.jl index fd39b49..95d96e5 100644 --- a/src/P232/problem.jl +++ b/src/P232/problem.jl @@ -3,7 +3,7 @@ module Problem232 title = "Problem 232: The Race" published_on = "Friday, 13th February 2009, 05:00 pm" -solved_by = 1819 +solved_by = 1827 difficulty_rating = "65%" content = """ Two players share an unbiased coin and take it in turns to play The Race. diff --git a/src/P233/problem.jl b/src/P233/problem.jl index f4c7ac0..8e01ed5 100644 --- a/src/P233/problem.jl +++ b/src/P233/problem.jl @@ -3,7 +3,7 @@ module Problem233 title = "Problem 233: Lattice points on a circle" published_on = "Friday, 20th February 2009, 09:00 pm" -solved_by = 2375 +solved_by = 2387 difficulty_rating = "70%" content = """ Let f(N) be the number of points with integer coordinates that are on a circle passing through (0,0), (N,0),(0,N), and (N,N). diff --git a/src/P234/problem.jl b/src/P234/problem.jl index 9abf8de..c9d8443 100644 --- a/src/P234/problem.jl +++ b/src/P234/problem.jl @@ -3,7 +3,7 @@ module Problem234 title = "Problem 234: Semidivisible numbers" published_on = "Saturday, 28th February 2009, 01:00 am" -solved_by = 3329 +solved_by = 3338 difficulty_rating = "50%" content = """ For an integer n ≥ 4, we define the lower prime square root of n, denoted by lps(n), as the largest prime ≤ √n and the upper diff --git a/src/P235/problem.jl b/src/P235/problem.jl index 5f4e78f..a6cae11 100644 --- a/src/P235/problem.jl +++ b/src/P235/problem.jl @@ -3,7 +3,7 @@ module Problem235 title = "Problem 235: An Arithmetic Geometric sequence" published_on = "Saturday, 7th March 2009, 05:00 am" -solved_by = 5095 +solved_by = 5111 difficulty_rating = "40%" content = """ Given is the arithmetic-geometric sequence u(k) = (900-3k)rᵏ⁻¹. diff --git a/src/P236/problem.jl b/src/P236/problem.jl index c194b9d..13adafc 100644 --- a/src/P236/problem.jl +++ b/src/P236/problem.jl @@ -3,7 +3,7 @@ module Problem236 title = "Problem 236: Luxury Hampers" published_on = "Saturday, 14th March 2009, 09:00 am" -solved_by = 958 +solved_by = 964 difficulty_rating = "80%" content = """ Suppliers 'A' and 'B' provided the following numbers of products for the luxury hamper market: diff --git a/src/P237/problem.jl b/src/P237/problem.jl index 72c49c4..8b23268 100644 --- a/src/P237/problem.jl +++ b/src/P237/problem.jl @@ -3,7 +3,7 @@ module Problem237 title = "Problem 237: Tours on a 4 x n playing board" published_on = "Saturday, 21st March 2009, 01:00 pm" -solved_by = 1601 +solved_by = 1610 difficulty_rating = "70%" content = """ Let T( diff --git a/src/P238/problem.jl b/src/P238/problem.jl index c1d9ef8..4cb2066 100644 --- a/src/P238/problem.jl +++ b/src/P238/problem.jl @@ -3,7 +3,7 @@ module Problem238 title = "Problem 238: Infinite string tour" published_on = "Sunday, 29th March 2009, 03:00 pm" -solved_by = 983 +solved_by = 989 difficulty_rating = "75%" content = """ Create a sequence of numbers using the "Blum Blum Shub" pseudo-random number generator: diff --git a/src/P239/problem.jl b/src/P239/problem.jl index 2012d02..e65046d 100644 --- a/src/P239/problem.jl +++ b/src/P239/problem.jl @@ -3,7 +3,7 @@ module Problem239 title = "Problem 239: Twenty-two Foolish Primes" published_on = "Friday, 3rd April 2009, 05:00 pm" -solved_by = 1866 +solved_by = 1872 difficulty_rating = "65%" content = """ A set of disks numbered 1 through 100 are placed in a line in random order. diff --git a/src/P24/problem.jl b/src/P24/problem.jl index b46edfb..c662691 100644 --- a/src/P24/problem.jl +++ b/src/P24/problem.jl @@ -3,7 +3,7 @@ module Problem24 title = "Problem 24: Lexicographic permutations" published_on = "Friday, 16th August 2002, 06:00 pm" -solved_by = 118646 +solved_by = 118781 difficulty_rating = "5%" content = """ A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. diff --git a/src/P240/problem.jl b/src/P240/problem.jl index ee6ec80..db1e2d5 100644 --- a/src/P240/problem.jl +++ b/src/P240/problem.jl @@ -3,7 +3,7 @@ module Problem240 title = "Problem 240: Top Dice" published_on = "Friday, 10th April 2009, 10:00 pm" -solved_by = 2236 +solved_by = 2237 difficulty_rating = "60%" content = """ There are 1111 ways in which five 6-sided dice (sides numbered 1 to 6) can be rolled so that the top three sum to 15. Some diff --git a/src/P241/problem.jl b/src/P241/problem.jl index 3bcd30a..ea875db 100644 --- a/src/P241/problem.jl +++ b/src/P241/problem.jl @@ -3,7 +3,7 @@ module Problem241 title = "Problem 241: Perfection Quotients" published_on = "Saturday, 18th April 2009, 02:00 am" -solved_by = 953 +solved_by = 956 difficulty_rating = "80%" content = """ For a positive integer n, let \\sigma(n) be the sum of all divisors of n. For example, \\sigma(6) = 1 + 2 + 3 + 6 = 12. diff --git a/src/P242/problem.jl b/src/P242/problem.jl index 17426af..2f746f2 100644 --- a/src/P242/problem.jl +++ b/src/P242/problem.jl @@ -3,7 +3,7 @@ module Problem242 title = "Problem 242: Odd Triplets" published_on = "Saturday, 25th April 2009, 06:00 am" -solved_by = 1068 +solved_by = 1073 difficulty_rating = "75%" content = """ Given the set {1,2,...,n}, we define f(n,k) as the number of its k-element subsets with an odd sum of elements. For example, diff --git a/src/P243/problem.jl b/src/P243/problem.jl index 459cf95..98563c8 100644 --- a/src/P243/problem.jl +++ b/src/P243/problem.jl @@ -3,7 +3,7 @@ module Problem243 title = "Problem 243: Resilience" published_on = "Saturday, 2nd May 2009, 10:00 am" -solved_by = 9771 +solved_by = 9802 difficulty_rating = "35%" content = """ A positive fraction whose numerator is less than its denominator is called a proper fraction. diff --git a/src/P244/problem.jl b/src/P244/problem.jl index ad525e6..f4c6c17 100644 --- a/src/P244/problem.jl +++ b/src/P244/problem.jl @@ -3,7 +3,7 @@ module Problem244 title = "Problem 244: Sliders" published_on = "Saturday, 9th May 2009, 02:00 pm" -solved_by = 1345 +solved_by = 1355 difficulty_rating = "70%" content = """ You probably know the game diff --git a/src/P245/problem.jl b/src/P245/problem.jl index 501446d..4621575 100644 --- a/src/P245/problem.jl +++ b/src/P245/problem.jl @@ -3,7 +3,7 @@ module Problem245 title = "Problem 245: Coresilience" published_on = "Friday, 15th May 2009, 02:00 pm" -solved_by = 829 +solved_by = 837 difficulty_rating = "80%" content = """ We shall call a fraction that cannot be cancelled down a resilient fraction. diff --git a/src/P246/problem.jl b/src/P246/problem.jl index 41e347e..4f8205f 100644 --- a/src/P246/problem.jl +++ b/src/P246/problem.jl @@ -3,7 +3,7 @@ module Problem246 title = "Problem 246: Tangents to an ellipse" published_on = "Friday, 22nd May 2009, 05:00 pm" -solved_by = 818 +solved_by = 821 difficulty_rating = "80%" content = """ diff --git a/src/P247/problem.jl b/src/P247/problem.jl index 2fc58be..5d1559d 100644 --- a/src/P247/problem.jl +++ b/src/P247/problem.jl @@ -3,7 +3,7 @@ module Problem247 title = "Problem 247: Squares under a hyperbola" published_on = "Friday, 29th May 2009, 09:00 pm" -solved_by = 1491 +solved_by = 1507 difficulty_rating = "65%" content = """ Consider the region constrained by 1 ≤ diff --git a/src/P248/problem.jl b/src/P248/problem.jl index 848d8a8..6ce038d 100644 --- a/src/P248/problem.jl +++ b/src/P248/problem.jl @@ -3,7 +3,7 @@ module Problem248 title = "Problem 248: Numbers for which Euler’s totient function equals 13!" published_on = "Saturday, 6th June 2009, 01:00 am" -solved_by = 1326 +solved_by = 1330 difficulty_rating = "70%" content = """ The first number n for which φ(n)=13! is 6227180929. diff --git a/src/P249/problem.jl b/src/P249/problem.jl index 77a9521..2f8a08c 100644 --- a/src/P249/problem.jl +++ b/src/P249/problem.jl @@ -3,7 +3,7 @@ module Problem249 title = "Problem 249: Prime Subset Sums" published_on = "Saturday, 13th June 2009, 05:00 am" -solved_by = 2590 +solved_by = 2600 difficulty_rating = "60%" content = """ Let S = {2, 3, 5, ..., 4999} be the set of prime numbers less than 5000. diff --git a/src/P25/problem.jl b/src/P25/problem.jl index 718846c..735372b 100644 --- a/src/P25/problem.jl +++ b/src/P25/problem.jl @@ -3,7 +3,7 @@ module Problem25 title = "Problem 25: 1000-digit Fibonacci number" published_on = "Friday, 30th August 2002, 06:00 pm" -solved_by = 160128 +solved_by = 160305 difficulty_rating = "5%" content = """ The Fibonacci sequence is defined by the recurrence relation: diff --git a/src/P250/problem.jl b/src/P250/problem.jl index 4904cbf..7155937 100644 --- a/src/P250/problem.jl +++ b/src/P250/problem.jl @@ -3,7 +3,7 @@ module Problem250 title = "Problem 250: 250250" published_on = "Saturday, 13th June 2009, 05:00 am" -solved_by = 3046 +solved_by = 3058 difficulty_rating = "55%" content = """ Find the number of non-empty subsets of {1¹, 2², 3³,..., 250250²⁵⁰²⁵⁰}, the sum of whose elements is divisible by 250. Enter diff --git a/src/P251/problem.jl b/src/P251/problem.jl index 0963639..04d287e 100644 --- a/src/P251/problem.jl +++ b/src/P251/problem.jl @@ -3,7 +3,7 @@ module Problem251 title = "Problem 251: Cardano Triplets" published_on = "Saturday, 20th June 2009, 09:00 am" -solved_by = 1419 +solved_by = 1424 difficulty_rating = "70%" content = """ diff --git a/src/P252/problem.jl b/src/P252/problem.jl index 22253e2..a3f8121 100644 --- a/src/P252/problem.jl +++ b/src/P252/problem.jl @@ -3,7 +3,7 @@ module Problem252 title = "Problem 252: Convex Holes" published_on = "Saturday, 27th June 2009, 01:00 pm" -solved_by = 852 +solved_by = 859 difficulty_rating = "80%" content = """ diff --git a/src/P253/problem.jl b/src/P253/problem.jl index c602e04..a93d7c3 100644 --- a/src/P253/problem.jl +++ b/src/P253/problem.jl @@ -3,7 +3,7 @@ module Problem253 title = "Problem 253: Tidying up A" published_on = "Friday, 28th August 2009, 01:00 pm" -solved_by = 1042 +solved_by = 1048 difficulty_rating = "75%" content = """ A small child has a “number caterpillar” consisting of forty jigsaw pieces, each with one number on it, which, when connected diff --git a/src/P254/problem.jl b/src/P254/problem.jl index 90a8ec0..8b3570a 100644 --- a/src/P254/problem.jl +++ b/src/P254/problem.jl @@ -3,7 +3,7 @@ module Problem254 title = "Problem 254: Sums of Digit Factorials" published_on = "Friday, 4th September 2009, 05:00 pm" -solved_by = 980 +solved_by = 987 difficulty_rating = "75%" content = """ Define f(n) as the sum of the factorials of the digits of n. For example, f(342) = 3! + 4! + 2! = 32. diff --git a/src/P255/problem.jl b/src/P255/problem.jl index 8beecb6..1af3a52 100644 --- a/src/P255/problem.jl +++ b/src/P255/problem.jl @@ -3,7 +3,7 @@ module Problem255 title = "Problem 255: Rounded Square Roots" published_on = "Friday, 11th September 2009, 09:00 pm" -solved_by = 881 +solved_by = 886 difficulty_rating = "75%" content = """ We define the diff --git a/src/P256/problem.jl b/src/P256/problem.jl index de00ec0..0026c7b 100644 --- a/src/P256/problem.jl +++ b/src/P256/problem.jl @@ -3,7 +3,7 @@ module Problem256 title = "Problem 256: Tatami-Free Rooms" published_on = "Saturday, 19th September 2009, 01:00 am" -solved_by = 749 +solved_by = 750 difficulty_rating = "80%" content = """ Tatami are rectangular mats, used to completely cover the floor of a room, without overlap. diff --git a/src/P257/problem.jl b/src/P257/problem.jl index 654eca1..8c6ba18 100644 --- a/src/P257/problem.jl +++ b/src/P257/problem.jl @@ -3,7 +3,7 @@ module Problem257 title = "Problem 257: Angular Bisectors" published_on = "Saturday, 26th September 2009, 05:00 am" -solved_by = 703 +solved_by = 705 difficulty_rating = "85%" content = """ Given is an integer sided triangle ABC with sides a ≤ b ≤ c. diff --git a/src/P258/problem.jl b/src/P258/problem.jl index 1fd3b8b..cc48239 100644 --- a/src/P258/problem.jl +++ b/src/P258/problem.jl @@ -3,7 +3,7 @@ module Problem258 title = "Problem 258: A lagged Fibonacci sequence" published_on = "Saturday, 3rd October 2009, 09:00 am" -solved_by = 1640 +solved_by = 1645 difficulty_rating = "70%" content = """ A sequence is defined as: diff --git a/src/P259/problem.jl b/src/P259/problem.jl index 352a8e9..5afabee 100644 --- a/src/P259/problem.jl +++ b/src/P259/problem.jl @@ -3,7 +3,7 @@ module Problem259 title = "Problem 259: Reachable Numbers" published_on = "Saturday, 10th October 2009, 01:00 pm" -solved_by = 1541 +solved_by = 1546 difficulty_rating = "70%" content = """ A positive integer will be called reachable if it can result from an arithmetic expression obeying the following rules: diff --git a/src/P26/problem.jl b/src/P26/problem.jl index 2607495..75edac6 100644 --- a/src/P26/problem.jl +++ b/src/P26/problem.jl @@ -3,7 +3,7 @@ module Problem26 title = "Problem 26: Reciprocal cycles" published_on = "Friday, 13th September 2002, 06:00 pm" -solved_by = 87326 +solved_by = 87456 difficulty_rating = "5%" content = """ A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given: diff --git a/src/P260/problem.jl b/src/P260/problem.jl index 4d4a907..04209d2 100644 --- a/src/P260/problem.jl +++ b/src/P260/problem.jl @@ -3,7 +3,7 @@ module Problem260 title = "Problem 260: Stone Game" published_on = "Friday, 16th October 2009, 01:00 pm" -solved_by = 1341 +solved_by = 1343 difficulty_rating = "70%" content = """ A game is played with three piles of stones and two players. diff --git a/src/P261/problem.jl b/src/P261/problem.jl index fb8aafd..9a960c3 100644 --- a/src/P261/problem.jl +++ b/src/P261/problem.jl @@ -3,7 +3,7 @@ module Problem261 title = "Problem 261: Pivotal Square Sums" published_on = "Friday, 23rd October 2009, 05:00 pm" -solved_by = 707 +solved_by = 713 difficulty_rating = "85%" content = """ Let us call a positive integer k a square-pivot, if there is a pair of integers m > 0 and n ≥ k, such that the sum of the (m+1) diff --git a/src/P262/problem.jl b/src/P262/problem.jl index 9d8987b..7860ca6 100644 --- a/src/P262/problem.jl +++ b/src/P262/problem.jl @@ -3,7 +3,7 @@ module Problem262 title = "Problem 262: Mountain Range" published_on = "Friday, 30th October 2009, 09:00 pm" -solved_by = 741 +solved_by = 742 difficulty_rating = "80%" content = """ The following equation represents the diff --git a/src/P263/problem.jl b/src/P263/problem.jl index 425678f..f5b19a9 100644 --- a/src/P263/problem.jl +++ b/src/P263/problem.jl @@ -3,7 +3,7 @@ module Problem263 title = "Problem 263: An engineers' dream come true" published_on = "Saturday, 7th November 2009, 01:00 am" -solved_by = 1065 +solved_by = 1068 difficulty_rating = "75%" content = """ Consider the number 6. The divisors of 6 are: 1,2,3 and 6. diff --git a/src/P264/problem.jl b/src/P264/problem.jl index a311c50..d0fe198 100644 --- a/src/P264/problem.jl +++ b/src/P264/problem.jl @@ -3,7 +3,7 @@ module Problem264 title = "Problem 264: Triangle Centres" published_on = "Saturday, 14th November 2009, 05:00 am" -solved_by = 581 +solved_by = 583 difficulty_rating = "85%" content = """ Consider all the triangles having: diff --git a/src/P265/problem.jl b/src/P265/problem.jl index 6a2cab7..1d5dbaa 100644 --- a/src/P265/problem.jl +++ b/src/P265/problem.jl @@ -3,7 +3,7 @@ module Problem265 title = "Problem 265: Binary Circles" published_on = "Saturday, 21st November 2009, 09:00 am" -solved_by = 4305 +solved_by = 4313 difficulty_rating = "40%" content = """ 2 diff --git a/src/P266/problem.jl b/src/P266/problem.jl index 5da443e..a52b655 100644 --- a/src/P266/problem.jl +++ b/src/P266/problem.jl @@ -3,7 +3,7 @@ module Problem266 title = "Problem 266: Pseudo Square Root" published_on = "Saturday, 28th November 2009, 01:00 pm" -solved_by = 1739 +solved_by = 1744 difficulty_rating = "65%" content = """ The divisors of 12 are: 1,2,3,4,6 and 12. diff --git a/src/P267/problem.jl b/src/P267/problem.jl index a258a70..6576df9 100644 --- a/src/P267/problem.jl +++ b/src/P267/problem.jl @@ -3,7 +3,7 @@ module Problem267 title = "Problem 267: Billionaire" published_on = "Friday, 4th December 2009, 01:00 pm" -solved_by = 3485 +solved_by = 3500 difficulty_rating = "50%" content = """ You are given a unique investment opportunity. diff --git a/src/P268/problem.jl b/src/P268/problem.jl index 690560c..31e4395 100644 --- a/src/P268/problem.jl +++ b/src/P268/problem.jl @@ -3,7 +3,7 @@ module Problem268 title = "Problem 268: Counting numbers with at least four distinct prime factors less than 100" published_on = "Friday, 11th December 2009, 05:00 pm" -solved_by = 1482 +solved_by = 1492 difficulty_rating = "70%" content = """ It can be verified that there are 23 positive integers less than 1000 that are divisible by at least four distinct primes less than diff --git a/src/P269/problem.jl b/src/P269/problem.jl index c226caa..cf3b6ac 100644 --- a/src/P269/problem.jl +++ b/src/P269/problem.jl @@ -3,7 +3,7 @@ module Problem269 title = "Problem 269: Polynomials with at least one integer root" published_on = "Saturday, 19th December 2009, 09:00 am" -solved_by = 708 +solved_by = 718 difficulty_rating = "80%" content = """ A root or zero of a polynomial P(x) is a solution to the equation P(x) = 0. diff --git a/src/P27/problem.jl b/src/P27/problem.jl index cf50ce4..d0d807c 100644 --- a/src/P27/problem.jl +++ b/src/P27/problem.jl @@ -3,7 +3,7 @@ module Problem27 title = "Problem 27: Quadratic primes" published_on = "Friday, 27th September 2002, 06:00 pm" -solved_by = 90744 +solved_by = 90864 difficulty_rating = "5%" content = """ Euler discovered the remarkable quadratic formula: diff --git a/src/P270/problem.jl b/src/P270/problem.jl index 45052a8..eb9348e 100644 --- a/src/P270/problem.jl +++ b/src/P270/problem.jl @@ -3,7 +3,7 @@ module Problem270 title = "Problem 270: Cutting Squares" published_on = "Saturday, 26th December 2009, 01:00 am" -solved_by = 655 +solved_by = 658 difficulty_rating = "80%" content = """ A square piece of paper with integer dimensions N×N is placed with a corner at the origin and two of its sides along the diff --git a/src/P271/problem.jl b/src/P271/problem.jl index 689371b..b05343f 100644 --- a/src/P271/problem.jl +++ b/src/P271/problem.jl @@ -3,7 +3,7 @@ module Problem271 title = "Problem 271: Modular Cubes, part 1" published_on = "Saturday, 2nd January 2010, 05:00 am" -solved_by = 2433 +solved_by = 2443 difficulty_rating = "60%" content = """ For a positive number n, define S(n) as the sum of the integers x, for which 1 1 coprime to 10 there is a positive divisibility multiplier m < p which preserves divisibility by p for the diff --git a/src/P275/problem.jl b/src/P275/problem.jl index 8ecd1fe..7cfcaa8 100644 --- a/src/P275/problem.jl +++ b/src/P275/problem.jl @@ -3,7 +3,7 @@ module Problem275 title = "Problem 275: Balanced Sculptures" published_on = "Friday, 22nd January 2010, 05:00 pm" -solved_by = 621 +solved_by = 624 difficulty_rating = "85%" content = """ Let us define a diff --git a/src/P276/problem.jl b/src/P276/problem.jl index 91336df..49cbca8 100644 --- a/src/P276/problem.jl +++ b/src/P276/problem.jl @@ -3,7 +3,7 @@ module Problem276 title = "Problem 276: Primitive Triangles" published_on = "Friday, 29th January 2010, 09:00 pm" -solved_by = 1116 +solved_by = 1120 difficulty_rating = "75%" content = """ Consider the triangles with integer sides a, b and c with a ≤ b ≤ c. diff --git a/src/P277/problem.jl b/src/P277/problem.jl index 1e64fb7..49260f1 100644 --- a/src/P277/problem.jl +++ b/src/P277/problem.jl @@ -3,7 +3,7 @@ module Problem277 title = "Problem 277: A Modified Collatz sequence" published_on = "Saturday, 6th February 2010, 01:00 am" -solved_by = 3300 +solved_by = 3314 difficulty_rating = "35%" content = """ diff --git a/src/P278/problem.jl b/src/P278/problem.jl index d0d71df..5beca1d 100644 --- a/src/P278/problem.jl +++ b/src/P278/problem.jl @@ -3,7 +3,7 @@ module Problem278 title = "Problem 278: Linear Combinations of Semiprimes" published_on = "Saturday, 13th February 2010, 05:00 am" -solved_by = 1071 +solved_by = 1075 difficulty_rating = "50%" content = """ diff --git a/src/P279/problem.jl b/src/P279/problem.jl index b0d3b2d..3615122 100644 --- a/src/P279/problem.jl +++ b/src/P279/problem.jl @@ -3,7 +3,7 @@ module Problem279 title = "Problem 279: Triangles with integral sides and an integral angle" published_on = "Saturday, 20th February 2010, 09:00 am" -solved_by = 755 +solved_by = 759 difficulty_rating = "60%" content = """ How many triangles are there with integral sides, at least one integral angle (measured in degrees), and a perimeter that does diff --git a/src/P28/problem.jl b/src/P28/problem.jl index 4f07349..9196852 100644 --- a/src/P28/problem.jl +++ b/src/P28/problem.jl @@ -3,7 +3,7 @@ module Problem28 title = "Problem 28: Number spiral diagonals" published_on = "Friday, 11th October 2002, 06:00 pm" -solved_by = 111672 +solved_by = 111801 difficulty_rating = "5%" content = """ Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: diff --git a/src/P280/problem.jl b/src/P280/problem.jl index a856bb6..e331fdf 100644 --- a/src/P280/problem.jl +++ b/src/P280/problem.jl @@ -3,7 +3,7 @@ module Problem280 title = "Problem 280: Ant and seeds" published_on = "Saturday, 27th February 2010, 01:00 pm" -solved_by = 1066 +solved_by = 1071 difficulty_rating = "65%" content = """ A laborious ant walks randomly on a 5x5 grid. The walk starts from the central square. At each step, the ant moves to an diff --git a/src/P281/problem.jl b/src/P281/problem.jl index f6d0a3e..78e8f88 100644 --- a/src/P281/problem.jl +++ b/src/P281/problem.jl @@ -3,7 +3,7 @@ module Problem281 title = "Problem 281: Pizza Toppings" published_on = "Friday, 5th March 2010, 01:00 pm" -solved_by = 1000 +solved_by = 1002 difficulty_rating = "55%" content = """ You are given a pizza (perfect circle) that has been cut into diff --git a/src/P282/problem.jl b/src/P282/problem.jl index 53e1763..cc6b11e 100644 --- a/src/P282/problem.jl +++ b/src/P282/problem.jl @@ -3,7 +3,7 @@ module Problem282 title = "Problem 282: The Ackermann function" published_on = "Friday, 12th March 2010, 05:00 pm" -solved_by = 1039 +solved_by = 1047 difficulty_rating = "70%" content = """ diff --git a/src/P283/problem.jl b/src/P283/problem.jl index e8475e5..333e19f 100644 --- a/src/P283/problem.jl +++ b/src/P283/problem.jl @@ -3,7 +3,7 @@ module Problem283 title = "Problem 283: Integer sided triangles for which the area/perimeter ratio is integral" published_on = "Friday, 19th March 2010, 09:00 pm" -solved_by = 650 +solved_by = 653 difficulty_rating = "75%" content = """ Consider the triangle with sides 6, 8 and 10. It can be seen that the perimeter and the area are both equal to 24. So the diff --git a/src/P284/problem.jl b/src/P284/problem.jl index ae9c661..54b2995 100644 --- a/src/P284/problem.jl +++ b/src/P284/problem.jl @@ -3,7 +3,7 @@ module Problem284 title = "Problem 284: Steady Squares" published_on = "Saturday, 27th March 2010, 01:00 am" -solved_by = 1280 +solved_by = 1287 difficulty_rating = "55%" content = """ The 3-digit number 376 in the decimal numbering system is an example of numbers with the special property that its square diff --git a/src/P285/problem.jl b/src/P285/problem.jl index dfa791f..dfaea62 100644 --- a/src/P285/problem.jl +++ b/src/P285/problem.jl @@ -3,7 +3,7 @@ module Problem285 title = "Problem 285: Pythagorean odds" published_on = "Saturday, 3rd April 2010, 05:00 am" -solved_by = 1240 +solved_by = 1252 difficulty_rating = "55%" content = """ Albert chooses a positive integer k, then two real numbers a, b are randomly chosen in the interval [0,1] with uniform diff --git a/src/P286/problem.jl b/src/P286/problem.jl index 03c990d..e3c321d 100644 --- a/src/P286/problem.jl +++ b/src/P286/problem.jl @@ -3,7 +3,7 @@ module Problem286 title = "Problem 286: Scoring probabilities" published_on = "Saturday, 3rd April 2010, 05:00 am" -solved_by = 2192 +solved_by = 2198 difficulty_rating = "50%" content = """ Barbara is a mathematician and a basketball player. She has found that the probability of scoring a point when shooting from a diff --git a/src/P287/problem.jl b/src/P287/problem.jl index caca221..fc7d114 100644 --- a/src/P287/problem.jl +++ b/src/P287/problem.jl @@ -3,7 +3,7 @@ module Problem287 title = "Problem 287: Quadtree encoding (a simple compression algorithm)" published_on = "Saturday, 10th April 2010, 09:00 am" -solved_by = 1473 +solved_by = 1482 difficulty_rating = "40%" content = """ The quadtree encoding allows us to describe a 2 diff --git a/src/P288/problem.jl b/src/P288/problem.jl index 49fd8bc..6c025ba 100644 --- a/src/P288/problem.jl +++ b/src/P288/problem.jl @@ -3,7 +3,7 @@ module Problem288 title = "Problem 288: An enormous factorial" published_on = "Saturday, 17th April 2010, 01:00 pm" -solved_by = 1690 +solved_by = 1693 difficulty_rating = "35%" content = """ For any prime p the number N(p,q) is defined by N(p,q) = ∑ₙ₌₀ ₜₒ _q Tₙ*pⁿ diff --git a/src/P289/problem.jl b/src/P289/problem.jl index accd78d..42dc810 100644 --- a/src/P289/problem.jl +++ b/src/P289/problem.jl @@ -3,7 +3,7 @@ module Problem289 title = "Problem 289: Eulerian Cycles" published_on = "Friday, 23rd April 2010, 01:00 pm" -solved_by = 506 +solved_by = 510 difficulty_rating = "90%" content = """ Let C( diff --git a/src/P29/problem.jl b/src/P29/problem.jl index fe24044..1ad403c 100644 --- a/src/P29/problem.jl +++ b/src/P29/problem.jl @@ -3,7 +3,7 @@ module Problem29 title = "Problem 29: Distinct powers" published_on = "Friday, 25th October 2002, 06:00 pm" -solved_by = 109160 +solved_by = 109318 difficulty_rating = "5%" content = """ Consider all integer combinations of aᵇ for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5: diff --git a/src/P290/problem.jl b/src/P290/problem.jl index 7572b48..eb5aee6 100644 --- a/src/P290/problem.jl +++ b/src/P290/problem.jl @@ -3,7 +3,7 @@ module Problem290 title = "Problem 290: Digital Signature" published_on = "Friday, 30th April 2010, 05:00 pm" -solved_by = 1004 +solved_by = 1009 difficulty_rating = "50%" content = """ How many integers 0 ≤ n < 10¹⁸ have the property that the sum of the digits of n equals the sum of digits of 137n? diff --git a/src/P291/problem.jl b/src/P291/problem.jl index ca49592..96adb1f 100644 --- a/src/P291/problem.jl +++ b/src/P291/problem.jl @@ -3,7 +3,7 @@ module Problem291 title = "Problem 291: Panaitopol Primes" published_on = "Friday, 7th May 2010, 09:00 pm" -solved_by = 1477 +solved_by = 1484 difficulty_rating = "45%" content = """ diff --git a/src/P292/problem.jl b/src/P292/problem.jl index 1996ad2..21eaf5f 100644 --- a/src/P292/problem.jl +++ b/src/P292/problem.jl @@ -3,7 +3,7 @@ module Problem292 title = "Problem 292: Pythagorean Polygons" published_on = "Saturday, 15th May 2010, 01:00 am" -solved_by = 580 +solved_by = 584 difficulty_rating = "65%" content = """ We shall define a pythagorean polygon to be a \e[1mconvex polygon\e[0m with the following properties: diff --git a/src/P293/problem.jl b/src/P293/problem.jl index fc60b0b..6bdbd61 100644 --- a/src/P293/problem.jl +++ b/src/P293/problem.jl @@ -3,7 +3,7 @@ module Problem293 title = "Problem 293: Pseudo-Fortunate Numbers" published_on = "Saturday, 22nd May 2010, 05:00 am" -solved_by = 3043 +solved_by = 3055 difficulty_rating = "30%" content = """ An even positive integer N will be called admissible, if it is a power of 2 or its distinct prime factors are consecutive primes. diff --git a/src/P294/problem.jl b/src/P294/problem.jl index fd10b81..127faf8 100644 --- a/src/P294/problem.jl +++ b/src/P294/problem.jl @@ -3,7 +3,7 @@ module Problem294 title = "Problem 294: Sum of digits - experience #23" published_on = "Saturday, 29th May 2010, 09:00 am" -solved_by = 938 +solved_by = 949 difficulty_rating = "45%" content = """ For a positive integer k, define d(k) as the sum of the digits of k in its usual decimal representation. Thus d(42) = 4+2 = 6. diff --git a/src/P295/problem.jl b/src/P295/problem.jl index f83380d..49294d3 100644 --- a/src/P295/problem.jl +++ b/src/P295/problem.jl @@ -3,7 +3,7 @@ module Problem295 title = "Problem 295: Lenticular holes" published_on = "Saturday, 5th June 2010, 01:00 pm" -solved_by = 465 +solved_by = 466 difficulty_rating = "75%" content = """ We call the convex area enclosed by two circles a diff --git a/src/P296/problem.jl b/src/P296/problem.jl index af34564..8c9e8fd 100644 --- a/src/P296/problem.jl +++ b/src/P296/problem.jl @@ -3,7 +3,7 @@ module Problem296 title = "Problem 296: Angular Bisector and Tangent" published_on = "Friday, 11th June 2010, 01:00 pm" -solved_by = 596 +solved_by = 597 difficulty_rating = "60%" content = """ diff --git a/src/P297/problem.jl b/src/P297/problem.jl index 30aea71..90d5884 100644 --- a/src/P297/problem.jl +++ b/src/P297/problem.jl @@ -3,7 +3,7 @@ module Problem297 title = "Problem 297: Zeckendorf Representation" published_on = "Friday, 18th June 2010, 05:00 pm" -solved_by = 2840 +solved_by = 2844 difficulty_rating = "35%" content = """ Each new term in the Fibonacci sequence is generated by adding the previous two terms. diff --git a/src/P298/problem.jl b/src/P298/problem.jl index ecc7375..3944feb 100644 --- a/src/P298/problem.jl +++ b/src/P298/problem.jl @@ -3,7 +3,7 @@ module Problem298 title = "Problem 298: Selective Amnesia" published_on = "Friday, 25th June 2010, 09:00 pm" -solved_by = 682 +solved_by = 685 difficulty_rating = "60%" content = """ Larry and Robin play a memory game involving a sequence of random numbers between 1 and 10, inclusive, that are called diff --git a/src/P3/problem.jl b/src/P3/problem.jl index 93cd907..b3b9d75 100644 --- a/src/P3/problem.jl +++ b/src/P3/problem.jl @@ -3,7 +3,7 @@ module Problem3 title = "Problem 3: Largest prime factor" published_on = "Friday, 2nd November 2001, 06:00 pm" -solved_by = 557861 +solved_by = 558101 difficulty_rating = "5%" content = """ The prime factors of 13195 are 5, 7, 13 and 29. diff --git a/src/P30/problem.jl b/src/P30/problem.jl index 0001483..2e54934 100644 --- a/src/P30/problem.jl +++ b/src/P30/problem.jl @@ -3,7 +3,7 @@ module Problem30 title = "Problem 30: Digit fifth powers" published_on = "Friday, 8th November 2002, 06:00 pm" -solved_by = 113742 +solved_by = 113892 difficulty_rating = "5%" content = """ Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: diff --git a/src/P300/problem.jl b/src/P300/problem.jl index 7cadad5..1f3d4d1 100644 --- a/src/P300/problem.jl +++ b/src/P300/problem.jl @@ -3,7 +3,7 @@ module Problem300 title = "Problem 300: Protein folding" published_on = "Saturday, 4th September 2010, 01:00 pm" -solved_by = 1124 +solved_by = 1132 difficulty_rating = "50%" content = """ In a very simplified form, we can consider proteins as strings consisting of hydrophobic (H) and polar (P) elements, e.g. HHPPHHHPHHPH. diff --git a/src/P301/problem.jl b/src/P301/problem.jl index 7cb6bac..0524315 100644 --- a/src/P301/problem.jl +++ b/src/P301/problem.jl @@ -3,7 +3,7 @@ module Problem301 title = "Problem 301: Nim" published_on = "Saturday, 11th September 2010, 04:00 pm" -solved_by = 6642 +solved_by = 6661 difficulty_rating = "15%" content = """ Nim is a game played with heaps of stones, where two players take it in turn to remove any number of stones from any heap diff --git a/src/P302/problem.jl b/src/P302/problem.jl index afdb7af..2a06dd0 100644 --- a/src/P302/problem.jl +++ b/src/P302/problem.jl @@ -3,7 +3,7 @@ module Problem302 title = "Problem 302: Strong Achilles Numbers" published_on = "Saturday, 18th September 2010, 07:00 pm" -solved_by = 760 +solved_by = 763 difficulty_rating = "60%" content = """ A positive integer n is \e[1mpowerful\e[0m if p² is a divisor of n for every prime factor p in n. diff --git a/src/P303/problem.jl b/src/P303/problem.jl index 26d36e3..8371252 100644 --- a/src/P303/problem.jl +++ b/src/P303/problem.jl @@ -3,7 +3,7 @@ module Problem303 title = "Problem 303: Multiples with small digits" published_on = "Saturday, 25th September 2010, 10:00 pm" -solved_by = 3700 +solved_by = 3712 difficulty_rating = "35%" content = """ diff --git a/src/P304/problem.jl b/src/P304/problem.jl index 6feb445..4917982 100644 --- a/src/P304/problem.jl +++ b/src/P304/problem.jl @@ -3,7 +3,7 @@ module Problem304 title = "Problem 304: Primonacci" published_on = "Sunday, 3rd October 2010, 01:00 am" -solved_by = 2230 +solved_by = 2240 difficulty_rating = "40%" content = """ For any positive integer n the function next_prime(n) returns the smallest prime p diff --git a/src/P305/problem.jl b/src/P305/problem.jl index 7b95495..270d952 100644 --- a/src/P305/problem.jl +++ b/src/P305/problem.jl @@ -3,7 +3,7 @@ module Problem305 title = "Problem 305: Reflexive Position" published_on = "Sunday, 10th October 2010, 04:00 am" -solved_by = 620 +solved_by = 622 difficulty_rating = "60%" content = """ Let's call S the (infinite) string that is made by concatenating the consecutive positive integers (starting from 1) written down in diff --git a/src/P306/problem.jl b/src/P306/problem.jl index e54e94a..146eb3b 100644 --- a/src/P306/problem.jl +++ b/src/P306/problem.jl @@ -3,7 +3,7 @@ module Problem306 title = "Problem 306: Paper-strip Game" published_on = "Sunday, 17th October 2010, 07:00 am" -solved_by = 1231 +solved_by = 1239 difficulty_rating = "55%" content = """ The following game is a classic example of Combinatorial Game Theory: diff --git a/src/P307/problem.jl b/src/P307/problem.jl index dd62579..9b0e2ea 100644 --- a/src/P307/problem.jl +++ b/src/P307/problem.jl @@ -3,7 +3,7 @@ module Problem307 title = "Problem 307: Chip Defects" published_on = "Sunday, 24th October 2010, 10:00 am" -solved_by = 1693 +solved_by = 1700 difficulty_rating = "40%" content = """ k defects are randomly distributed amongst n integrated-circuit chips produced by a factory (any number of defects may be diff --git a/src/P308/problem.jl b/src/P308/problem.jl index 80476d8..de9d1c8 100644 --- a/src/P308/problem.jl +++ b/src/P308/problem.jl @@ -3,7 +3,7 @@ module Problem308 title = "Problem 308: An amazing Prime-generating Automaton" published_on = "Saturday, 30th October 2010, 01:00 pm" -solved_by = 780 +solved_by = 784 difficulty_rating = "60%" content = """ A program written in the programming language Fractran consists of a list of fractions. diff --git a/src/P309/problem.jl b/src/P309/problem.jl index e1ddd93..2e6701e 100644 --- a/src/P309/problem.jl +++ b/src/P309/problem.jl @@ -3,7 +3,7 @@ module Problem309 title = "Problem: 309 Integer Ladders" published_on = "Saturday, 6th November 2010, 04:00 pm" -solved_by = 833 +solved_by = 837 difficulty_rating = "50%" content = """ In the classic "Crossing Ladders" problem, we are given the lengths diff --git a/src/P31/problem.jl b/src/P31/problem.jl index 1e819bf..7ad5147 100644 --- a/src/P31/problem.jl +++ b/src/P31/problem.jl @@ -3,7 +3,7 @@ module Problem31 title = "Problem 31: Coin sums" published_on = "Friday, 22nd November 2002, 06:00 pm" -solved_by = 88390 +solved_by = 88516 difficulty_rating = "5%" content = """ In the United Kingdom the currency is made up of pound (£) and pence (p). There are eight coins in general circulation: diff --git a/src/P310/problem.jl b/src/P310/problem.jl index 517135c..fb37f25 100644 --- a/src/P310/problem.jl +++ b/src/P310/problem.jl @@ -3,7 +3,7 @@ module Problem310 title = "Problem 310: Nim Square" published_on = "Saturday, 13th November 2010, 07:00 pm" -solved_by = 1174 +solved_by = 1181 difficulty_rating = "40%" content = """ Alice and Bob play the game Nim Square. diff --git a/src/P312/problem.jl b/src/P312/problem.jl index af9674b..0e9bf34 100644 --- a/src/P312/problem.jl +++ b/src/P312/problem.jl @@ -3,7 +3,7 @@ module Problem312 title = "Problem 312: Cyclic paths on Sierpiński graphs" published_on = "Sunday, 28th November 2010, 01:00 am" -solved_by = 858 +solved_by = 861 difficulty_rating = "50%" content = """ - A diff --git a/src/P313/problem.jl b/src/P313/problem.jl index 67b68bb..b696b5a 100644 --- a/src/P313/problem.jl +++ b/src/P313/problem.jl @@ -3,7 +3,7 @@ module Problem313 title = "Problem 313: Sliding game" published_on = "Sunday, 5th December 2010, 04:00 am" -solved_by = 1646 +solved_by = 1653 difficulty_rating = "30%" content = """ In a sliding game a counter may slide horizontally or vertically into an empty space. The objective of the game is to move the red counter from the top left corner of a grid to the bottom right corner; the space always starts in the bottom right corner. For example, the following sequence of pictures show how the game can be completed in five moves on a 2 by 2 grid. diff --git a/src/P314/problem.jl b/src/P314/problem.jl index 9b1b075..90bddd9 100644 --- a/src/P314/problem.jl +++ b/src/P314/problem.jl @@ -3,7 +3,7 @@ module Problem314 title = "Problem 314: The Mouse on the Moon" published_on = "Sunday, 12th December 2010, 07:00 am" -solved_by = 522 +solved_by = 524 difficulty_rating = "80%" content = """ diff --git a/src/P315/problem.jl b/src/P315/problem.jl index d154991..7c39c6c 100644 --- a/src/P315/problem.jl +++ b/src/P315/problem.jl @@ -3,7 +3,7 @@ module Problem315 title = "Problem 315: Digital root clocks" published_on = "Sunday, 19th December 2010, 10:00 am" -solved_by = 3477 +solved_by = 3493 difficulty_rating = "20%" content = """ Sam and Max are asked to transform two digital clocks into two "digital root" clocks. diff --git a/src/P316/problem.jl b/src/P316/problem.jl index 0a8fa20..a148e4f 100644 --- a/src/P316/problem.jl +++ b/src/P316/problem.jl @@ -3,7 +3,7 @@ module Problem316 title = "Problem 316: Numbers in decimal expansions" published_on = "Saturday, 25th December 2010, 01:00 pm" -solved_by = 682 +solved_by = 684 difficulty_rating = "55%" content = """ Let diff --git a/src/P317/problem.jl b/src/P317/problem.jl index 5c1cd65..494ace7 100644 --- a/src/P317/problem.jl +++ b/src/P317/problem.jl @@ -3,7 +3,7 @@ module Problem317 title = "Problem 317: Firecracker" published_on = "Saturday, 1st January 2011, 04:00 pm" -solved_by = 2729 +solved_by = 2742 difficulty_rating = "35%" content = """ A firecracker explodes at a height of 100 m above level ground. It breaks into a large number of very small fragments, which diff --git a/src/P318/problem.jl b/src/P318/problem.jl index ea285b7..f4e2f94 100644 --- a/src/P318/problem.jl +++ b/src/P318/problem.jl @@ -3,7 +3,7 @@ module Problem318 title = "Problem 318: 2011 nines" published_on = "Saturday, 1st January 2011, 04:00 pm" -solved_by = 959 +solved_by = 965 difficulty_rating = "50%" content = """ Consider the real number √2 + √3. diff --git a/src/P32/problem.jl b/src/P32/problem.jl index c67f246..d8fa430 100644 --- a/src/P32/problem.jl +++ b/src/P32/problem.jl @@ -3,7 +3,7 @@ module Problem32 title = "Problem 32: Pandigital products" published_on = "Friday, 6th December 2002, 06:00 pm" -solved_by = 74156 +solved_by = 74274 difficulty_rating = "5%" content = """ We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit diff --git a/src/P320/problem.jl b/src/P320/problem.jl index fd93aa3..5053915 100644 --- a/src/P320/problem.jl +++ b/src/P320/problem.jl @@ -3,7 +3,7 @@ module Problem320 title = "Problem 320: Factorials divisible by a huge integer" published_on = "Saturday, 15th January 2011, 10:00 pm" -solved_by = 886 +solved_by = 890 difficulty_rating = "50%" content = """ Let N(i) be the smallest integer n such that n! is divisible by (i!)¹²³⁴⁵⁶⁷⁸⁹⁰ diff --git a/src/P321/problem.jl b/src/P321/problem.jl index 3484f21..f27e252 100644 --- a/src/P321/problem.jl +++ b/src/P321/problem.jl @@ -3,7 +3,7 @@ module Problem321 title = "Problem 321: Swapping Counters" published_on = "Sunday, 23rd January 2011, 01:00 am" -solved_by = 1767 +solved_by = 1776 difficulty_rating = "30%" content = """ A horizontal row comprising of 2 diff --git a/src/P322/problem.jl b/src/P322/problem.jl index ac0dbdb..3c9f7d1 100644 --- a/src/P322/problem.jl +++ b/src/P322/problem.jl @@ -3,7 +3,7 @@ module Problem322 title = "Problem 322: Binomial coefficients divisible by 10" published_on = "Sunday, 30th January 2011, 04:00 am" -solved_by = 473 +solved_by = 477 difficulty_rating = "70%" content = """ Let T(m, n) be the number of the binomial coefficients ⁱCₙ that are divisible by 10 for n ≤ i < m(i, m and n are positive integers). diff --git a/src/P323/problem.jl b/src/P323/problem.jl index 0642094..b92711c 100644 --- a/src/P323/problem.jl +++ b/src/P323/problem.jl @@ -3,7 +3,7 @@ module Problem323 title = "Problem 32: Bitwise-OR operations on random integers" published_on = "Sunday, 6th February 2011, 07:00 am" -solved_by = 3982 +solved_by = 3991 difficulty_rating = "20%" content = """ Let y₀, y₁, y₂,... be a sequence of random unsigned 32 bit integers diff --git a/src/P324/problem.jl b/src/P324/problem.jl index cf494e2..b045bb9 100644 --- a/src/P324/problem.jl +++ b/src/P324/problem.jl @@ -3,7 +3,7 @@ module Problem324 title = "Problem 324: Building a tower" published_on = "Sunday, 13th February 2011, 10:00 am" -solved_by = 720 +solved_by = 726 difficulty_rating = "50%" content = """ Let f(n) represent the number of ways one can fill a 3×3×n tower with blocks of 2×1×1. diff --git a/src/P325/problem.jl b/src/P325/problem.jl index 324f452..dab39cc 100644 --- a/src/P325/problem.jl +++ b/src/P325/problem.jl @@ -3,7 +3,7 @@ module Problem325 title = "Problem 325: Stone Game II" published_on = "Saturday, 19th February 2011, 01:00 pm" -solved_by = 613 +solved_by = 614 difficulty_rating = "80%" content = """ A game is played with two piles of stones and two players. diff --git a/src/P326/problem.jl b/src/P326/problem.jl index d635090..d4c35f4 100644 --- a/src/P326/problem.jl +++ b/src/P326/problem.jl @@ -3,7 +3,7 @@ module Problem326 title = "Problem 326: Modulo Summations" published_on = "Saturday, 26th February 2011, 04:00 pm" -solved_by = 532 +solved_by = 540 difficulty_rating = "55%" content = """ diff --git a/src/P327/problem.jl b/src/P327/problem.jl index 99a3a56..60c73cc 100644 --- a/src/P327/problem.jl +++ b/src/P327/problem.jl @@ -3,7 +3,7 @@ module Problem327 title = "Problem 327: Rooms of Doom" published_on = "Saturday, 5th March 2011, 07:00 pm" -solved_by = 1153 +solved_by = 1160 difficulty_rating = "40%" content = """ A series of three rooms are connected to each other by automatic doors. diff --git a/src/P328/problem.jl b/src/P328/problem.jl index ba52d2b..f7f09a2 100644 --- a/src/P328/problem.jl +++ b/src/P328/problem.jl @@ -3,7 +3,7 @@ module Problem328 title = "Problem 328: Lowest-cost Search" published_on = "Saturday, 12th March 2011, 10:00 pm" -solved_by = 440 +solved_by = 441 difficulty_rating = "95%" content = """ We are trying to find a hidden number selected from the set of integers {1, 2, ..., diff --git a/src/P329/problem.jl b/src/P329/problem.jl index 20ab897..ef0ab1e 100644 --- a/src/P329/problem.jl +++ b/src/P329/problem.jl @@ -3,7 +3,7 @@ module Problem329 title = "Problem 329: Prime Frog" published_on = "Sunday, 20th March 2011, 01:00 am" -solved_by = 2569 +solved_by = 2582 difficulty_rating = "25%" content = """ Susan has a prime frog. diff --git a/src/P33/problem.jl b/src/P33/problem.jl index 05d29f4..0427dbd 100644 --- a/src/P33/problem.jl +++ b/src/P33/problem.jl @@ -3,7 +3,7 @@ module Problem33 title = "Problem 33: Digit cancelling fractions" published_on = "Friday, 20th December 2002, 06:00 pm" -solved_by = 74506 +solved_by = 74618 difficulty_rating = "5%" content = """ The fraction ⁴⁹/₉₈ is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe diff --git a/src/P330/problem.jl b/src/P330/problem.jl index 8f0cf8d..06906cb 100644 --- a/src/P330/problem.jl +++ b/src/P330/problem.jl @@ -3,7 +3,7 @@ module Problem330 title = "Problem 330: Euler's Number" published_on = "Sunday, 27th March 2011, 05:00 am" -solved_by = 539 +solved_by = 543 difficulty_rating = "70%" content = """ diff --git a/src/P331/problem.jl b/src/P331/problem.jl index 27e8674..7e79641 100644 --- a/src/P331/problem.jl +++ b/src/P331/problem.jl @@ -3,7 +3,7 @@ module Problem331 title = "Problem 331: Cross flips" published_on = "Sunday, 3rd April 2011, 08:00 am" -solved_by = 417 +solved_by = 420 difficulty_rating = "100%" content = """ N diff --git a/src/P332/problem.jl b/src/P332/problem.jl index 93698da..4df2bcf 100644 --- a/src/P332/problem.jl +++ b/src/P332/problem.jl @@ -3,7 +3,7 @@ module Problem332 title = "Problem 332: Spherical triangles" published_on = "Sunday, 10th April 2011, 10:00 am" -solved_by = 625 +solved_by = 631 difficulty_rating = "50%" content = """ A diff --git a/src/P333/problem.jl b/src/P333/problem.jl index 74d29c0..4cc4267 100644 --- a/src/P333/problem.jl +++ b/src/P333/problem.jl @@ -3,7 +3,7 @@ module Problem333 title = "Problem 333: Special partitions" published_on = "Saturday, 16th April 2011, 01:00 pm" -solved_by = 1263 +solved_by = 1270 difficulty_rating = "35%" content = """ All positive integers can be partitioned in such a way that each and every term of the partition can be expressed as 2ⁱx3ʲ, where diff --git a/src/P334/problem.jl b/src/P334/problem.jl index 5b845c6..380eac6 100644 --- a/src/P334/problem.jl +++ b/src/P334/problem.jl @@ -3,7 +3,7 @@ module Problem334 title = "Problem 334: Spilling the beans" published_on = "Saturday, 23rd April 2011, 04:00 pm" -solved_by = 485 +solved_by = 489 difficulty_rating = "65%" content = """ In Plato's heaven, there exist an infinite number of bowls in a straight line. diff --git a/src/P335/problem.jl b/src/P335/problem.jl index d1e52ed..353b29c 100644 --- a/src/P335/problem.jl +++ b/src/P335/problem.jl @@ -3,7 +3,7 @@ module Problem335 title = "Problem 335: Gathering the beans" published_on = "Saturday, 23rd April 2011, 04:00 pm" -solved_by = 521 +solved_by = 526 difficulty_rating = "65%" content = """ Whenever Peter feels bored, he places some bowls, containing one bean each, in a circle. After this, he takes all the beans out of a certain bowl and drops them one by one in the bowls going clockwise. He repeats this, starting from the bowl he dropped the last bean in, until the initial situation appears again. For example with 5 bowls he acts as follows: diff --git a/src/P336/problem.jl b/src/P336/problem.jl index 3eb390e..69afae8 100644 --- a/src/P336/problem.jl +++ b/src/P336/problem.jl @@ -3,7 +3,7 @@ module Problem336 title = "Problem 336: Maximix Arrangements" published_on = "Saturday, 30th April 2011, 07:00 pm" -solved_by = 2115 +solved_by = 2127 difficulty_rating = "25%" content = """ A train is used to transport four carriages in the order: ABCD. However, sometimes when the train arrives to collect the carriages they are not in the correct order. diff --git a/src/P337/problem.jl b/src/P337/problem.jl index 5162821..09a6520 100644 --- a/src/P337/problem.jl +++ b/src/P337/problem.jl @@ -3,7 +3,7 @@ module Problem337 title = "Problem 337: Totient Stairstep Sequences" published_on = "Saturday, 7th May 2011, 10:00 pm" -solved_by = 524 +solved_by = 528 difficulty_rating = "70%" content = """ Let {a₁, a₂,..., aₙ} be an integer sequence of length n such that: diff --git a/src/P338/problem.jl b/src/P338/problem.jl index 3ef98b0..d24166b 100644 --- a/src/P338/problem.jl +++ b/src/P338/problem.jl @@ -3,7 +3,7 @@ module Problem338 title = "Problem 338: Cutting Rectangular Grid Paper" published_on = "Sunday, 15th May 2011, 01:00 am" -solved_by = 333 +solved_by = 334 difficulty_rating = "95%" content = """ A rectangular sheet of grid paper with integer dimensions diff --git a/src/P339/problem.jl b/src/P339/problem.jl index d13f96b..0b60730 100644 --- a/src/P339/problem.jl +++ b/src/P339/problem.jl @@ -3,7 +3,7 @@ module Problem339 title = "Problem 339: Peredur fab Efrawg" published_on = "Sunday, 22nd May 2011, 04:00 am" -solved_by = 564 +solved_by = 569 difficulty_rating = "70%" content = """ "And he came towards a valley, through which ran a river; and the borders of the valley were wooded, and on each side of diff --git a/src/P34/problem.jl b/src/P34/problem.jl index 0314976..e607dcc 100644 --- a/src/P34/problem.jl +++ b/src/P34/problem.jl @@ -3,7 +3,7 @@ module Problem34 title = "Problem 34: Digit factorials" published_on = "Friday, 3rd January 2003, 06:00 pm" -solved_by = 97545 +solved_by = 97700 difficulty_rating = "5%" content = """ 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145. diff --git a/src/P340/problem.jl b/src/P340/problem.jl index a925d24..7e42c2c 100644 --- a/src/P340/problem.jl +++ b/src/P340/problem.jl @@ -3,7 +3,7 @@ module Problem340 title = "Problem 340: Crazy Function" published_on = "Sunday, 29th May 2011, 07:00 am" -solved_by = 1131 +solved_by = 1140 difficulty_rating = "30%" content = """ diff --git a/src/P341/problem.jl b/src/P341/problem.jl index f3b97d8..7228d86 100644 --- a/src/P341/problem.jl +++ b/src/P341/problem.jl @@ -3,7 +3,7 @@ module Problem341 title = "Problem 341: Golomb's self-describing sequence" published_on = "Sunday, 5th June 2011, 10:00 am" -solved_by = 950 +solved_by = 953 difficulty_rating = "45%" content = """ The Golomb's self-describing sequence (G(n)) is the only nondecreasing sequence of natural numbers such that n diff --git a/src/P342/problem.jl b/src/P342/problem.jl index 39a964d..ec89b4d 100644 --- a/src/P342/problem.jl +++ b/src/P342/problem.jl @@ -3,7 +3,7 @@ module Problem342 title = "Problem 342: The totient of a square is a cube" published_on = "Saturday, 11th June 2011, 01:00 pm" -solved_by = 809 +solved_by = 816 difficulty_rating = "50%" content = """ Consider the number 50. diff --git a/src/P343/problem.jl b/src/P343/problem.jl index e43ad9a..876220f 100644 --- a/src/P343/problem.jl +++ b/src/P343/problem.jl @@ -3,7 +3,7 @@ module Problem343 title = "Problem 343: Fractional Sequences" published_on = "Saturday, 18th June 2011, 04:00 pm" -solved_by = 1433 +solved_by = 1439 difficulty_rating = "35%" content = """ For any positive integer k, a finite sequence aᵢ of fractions xᵢ/yᵢ is defined by: diff --git a/src/P344/problem.jl b/src/P344/problem.jl index 949a6f4..56473b3 100644 --- a/src/P344/problem.jl +++ b/src/P344/problem.jl @@ -3,7 +3,7 @@ module Problem344 title = "Problem 344: Silver dollar game" published_on = "Saturday, 25th June 2011, 07:00 pm" -solved_by = 331 +solved_by = 330 difficulty_rating = "100%" content = """ One variant of N.G. de Bruijn's diff --git a/src/P345/problem.jl b/src/P345/problem.jl index f480056..f18b96b 100644 --- a/src/P345/problem.jl +++ b/src/P345/problem.jl @@ -3,7 +3,7 @@ module Problem345 title = "Problem 345: Matrix Sum" published_on = "Saturday, 3rd September 2011, 04:00 pm" -solved_by = 5813 +solved_by = 5839 difficulty_rating = "15%" content = """ We define the Matrix Sum of a matrix as the maximum possible sum of matrix elements such that none of the selected diff --git a/src/P346/problem.jl b/src/P346/problem.jl index a2684a1..3b71402 100644 --- a/src/P346/problem.jl +++ b/src/P346/problem.jl @@ -3,7 +3,7 @@ module Problem346 title = "Problem 346: Strong Repunits" published_on = "Saturday, 3rd September 2011, 04:00 pm" -solved_by = 4419 +solved_by = 4439 difficulty_rating = "15%" content = """ The number 7 is special, because 7 is 111 written in base 2, and 11 written in base 6 diff --git a/src/P347/problem.jl b/src/P347/problem.jl index 97420c8..8456e16 100644 --- a/src/P347/problem.jl +++ b/src/P347/problem.jl @@ -3,7 +3,7 @@ module Problem347 title = "Problem 347: Largest integer divisible by two primes" published_on = "Saturday, 3rd September 2011, 04:00 pm" -solved_by = 4687 +solved_by = 4701 difficulty_rating = "15%" content = """ The largest integer ≤ 100 that is only divisible by both the primes 2 and 3 is 96, as 96=32*3=2⁵*3. For two distinct primes p and diff --git a/src/P348/problem.jl b/src/P348/problem.jl index feb098c..77a0054 100644 --- a/src/P348/problem.jl +++ b/src/P348/problem.jl @@ -3,7 +3,7 @@ module Problem348 title = "Problem 348: Sum of a square and a cube" published_on = "Saturday, 3rd September 2011, 04:00 pm" -solved_by = 3115 +solved_by = 3129 difficulty_rating = "25%" content = """ Many numbers can be expressed as the sum of a square and a cube. Some of them in more than one way. diff --git a/src/P349/problem.jl b/src/P349/problem.jl index 97ce57a..c988f96 100644 --- a/src/P349/problem.jl +++ b/src/P349/problem.jl @@ -3,7 +3,7 @@ module Problem349 title = "Problem 349: Langton's ant" published_on = "Saturday, 3rd September 2011, 04:00 pm" -solved_by = 1961 +solved_by = 1972 difficulty_rating = "35%" content = """ An ant moves on a regular grid of squares that are coloured either black or white. diff --git a/src/P35/problem.jl b/src/P35/problem.jl index 255e93f..9d73933 100644 --- a/src/P35/problem.jl +++ b/src/P35/problem.jl @@ -3,7 +3,7 @@ module Problem35 title = "Problem 35: Circular primes" published_on = "Friday, 17th January 2003, 06:00 pm" -solved_by = 87808 +solved_by = 87929 difficulty_rating = "5%" content = """ The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. diff --git a/src/P350/problem.jl b/src/P350/problem.jl index 3fec190..9d5b5ab 100644 --- a/src/P350/problem.jl +++ b/src/P350/problem.jl @@ -3,7 +3,7 @@ module Problem350 title = "Problem 350: Constraining the least greatest and the greatest least" published_on = "Saturday, 10th September 2011, 07:00 pm" -solved_by = 469 +solved_by = 473 difficulty_rating = "60%" content = """ A list of size n is a sequence of n natural numbers. diff --git a/src/P351/problem.jl b/src/P351/problem.jl index 4539d71..41d30af 100644 --- a/src/P351/problem.jl +++ b/src/P351/problem.jl @@ -3,7 +3,7 @@ module Problem351 title = "Problem 351: Hexagonal orchards" published_on = "Saturday, 17th September 2011, 10:00 pm" -solved_by = 2626 +solved_by = 2632 difficulty_rating = "25%" content = """ A diff --git a/src/P352/problem.jl b/src/P352/problem.jl index 80374f4..1c369cb 100644 --- a/src/P352/problem.jl +++ b/src/P352/problem.jl @@ -3,7 +3,7 @@ module Problem352 title = "Problem 352: Blood tests" published_on = "Sunday, 2nd October 2011, 01:00 am" -solved_by = 619 +solved_by = 622 difficulty_rating = "55%" content = """ Each one of the 25 sheep in a flock must be tested for a rare virus, known to affect 2% of the sheep population. An accurate diff --git a/src/P353/problem.jl b/src/P353/problem.jl index 7f41a39..cffe6f6 100644 --- a/src/P353/problem.jl +++ b/src/P353/problem.jl @@ -3,7 +3,7 @@ module Problem353 title = "Problem 353: Risky moon" published_on = "Sunday, 9th October 2011, 04:00 am" -solved_by = 493 +solved_by = 496 difficulty_rating = "50%" content = """ diff --git a/src/P354/problem.jl b/src/P354/problem.jl index 11a3d66..e06261a 100644 --- a/src/P354/problem.jl +++ b/src/P354/problem.jl @@ -3,7 +3,7 @@ module Problem354 title = "Problem 354: Distances in a bee's honeycomb" published_on = "Sunday, 16th October 2011, 07:00 am" -solved_by = 450 +solved_by = 453 difficulty_rating = "65%" content = """ Consider a honey bee's honeycomb where each cell is a perfect regular hexagon with side length 1. diff --git a/src/P355/problem.jl b/src/P355/problem.jl index 9fd58f9..a667569 100644 --- a/src/P355/problem.jl +++ b/src/P355/problem.jl @@ -3,7 +3,7 @@ module Problem355 title = "Problem 355: Maximal coprime subset" published_on = "Sunday, 23rd October 2011, 10:00 am" -solved_by = 540 +solved_by = 544 difficulty_rating = "70%" content = """ Define Co(n) to be the maximal possible sum of a set of mutually co-prime elements from {1, 2, ..., n}. diff --git a/src/P356/problem.jl b/src/P356/problem.jl index d86b26a..20fc5bc 100644 --- a/src/P356/problem.jl +++ b/src/P356/problem.jl @@ -3,7 +3,7 @@ module Problem356 title = "Problem 356: Largest roots of cubic polynomials" published_on = "Saturday, 29th October 2011, 01:00 pm" -solved_by = 609 +solved_by = 611 difficulty_rating = "60%" content = """ diff --git a/src/P357/problem.jl b/src/P357/problem.jl index 3b836d1..b67a1c4 100644 --- a/src/P357/problem.jl +++ b/src/P357/problem.jl @@ -3,7 +3,7 @@ module Problem357 title = "Problem 357: Prime generating integers" published_on = "Saturday, 5th November 2011, 04:00 pm" -solved_by = 8342 +solved_by = 8365 difficulty_rating = "10%" content = """ Consider the divisors of 30: 1,2,3,5,6,10,15,30. diff --git a/src/P358/problem.jl b/src/P358/problem.jl index f9fb116..dc34eb9 100644 --- a/src/P358/problem.jl +++ b/src/P358/problem.jl @@ -3,7 +3,7 @@ module Problem358 title = "Problem 358: Cyclic numbers" published_on = "Saturday, 12th November 2011, 07:00 pm" -solved_by = 1647 +solved_by = 1661 difficulty_rating = "25%" content = """ A cyclic number with n digits has a very interesting property: diff --git a/src/P359/problem.jl b/src/P359/problem.jl index 2455283..5c222bb 100644 --- a/src/P359/problem.jl +++ b/src/P359/problem.jl @@ -3,7 +3,7 @@ module Problem359 title = "Problem 359: Hilbert's New Hotel" published_on = "Saturday, 19th November 2011, 10:00 pm" -solved_by = 1565 +solved_by = 1569 difficulty_rating = "25%" content = """ An infinite number of people (numbered 1, 2, 3, etc.) are lined up to get a room at Hilbert's newest infinite hotel. The hotel diff --git a/src/P36/problem.jl b/src/P36/problem.jl index ea967b0..01e96cb 100644 --- a/src/P36/problem.jl +++ b/src/P36/problem.jl @@ -3,7 +3,7 @@ module Problem36 title = "Problem 36: Double-base palindromes" published_on = "Friday, 31st January 2003, 06:00 pm" -solved_by = 91923 +solved_by = 92046 difficulty_rating = "5%" content = """ The decimal number, 585 = 1001001001₂ (binary), is palindromic in both bases. diff --git a/src/P360/problem.jl b/src/P360/problem.jl index ea05919..bf00e1e 100644 --- a/src/P360/problem.jl +++ b/src/P360/problem.jl @@ -3,7 +3,7 @@ module Problem360 title = "Problem 360: Scary Sphere" published_on = "Sunday, 27th November 2011, 01:00 am" -solved_by = 597 +solved_by = 600 difficulty_rating = "50%" content = """ Given two points (x₁,y₁,z₁) and (x₂,y₂,z₂) in three dimensional space, the \e[1mManhattan distance\e[0m between those points is defined diff --git a/src/P361/problem.jl b/src/P361/problem.jl index 022a255..23addfd 100644 --- a/src/P361/problem.jl +++ b/src/P361/problem.jl @@ -3,7 +3,7 @@ module Problem361 title = "Problem 361: Subsequence of Thue-Morse sequence" published_on = "Sunday, 4th December 2011, 04:00 am" -solved_by = 305 +solved_by = 310 difficulty_rating = "90%" content = """ The diff --git a/src/P362/problem.jl b/src/P362/problem.jl index a8c8314..7b7ea62 100644 --- a/src/P362/problem.jl +++ b/src/P362/problem.jl @@ -3,7 +3,7 @@ module Problem362 title = "Problem 362: Squarefree factors" published_on = "Sunday, 11th December 2011, 07:00 am" -solved_by = 480 +solved_by = 482 difficulty_rating = "70%" content = """ Consider the number 54. diff --git a/src/P363/problem.jl b/src/P363/problem.jl index 7dfead0..bc56d8b 100644 --- a/src/P363/problem.jl +++ b/src/P363/problem.jl @@ -3,7 +3,7 @@ module Problem363 title = "Problem 363: Bézier Curves" published_on = "Sunday, 18th December 2011, 10:00 am" -solved_by = 1141 +solved_by = 1146 difficulty_rating = "35%" content = """ A cubic Bézier curve is defined by four points: P_0, P_1, P_2, and P_3. diff --git a/src/P364/problem.jl b/src/P364/problem.jl index b47c7a0..d64c5a1 100644 --- a/src/P364/problem.jl +++ b/src/P364/problem.jl @@ -3,7 +3,7 @@ module Problem364 title = "Problem 364: Comfortable distance" published_on = "Saturday, 24th December 2011, 01:00 pm" -solved_by = 714 +solved_by = 720 difficulty_rating = "50%" content = """ diff --git a/src/P365/problem.jl b/src/P365/problem.jl index 6367dc6..003e06e 100644 --- a/src/P365/problem.jl +++ b/src/P365/problem.jl @@ -3,7 +3,7 @@ module Problem365 title = "Problem 365: A huge binomial coefficient" published_on = "Saturday, 31st December 2011, 04:00 pm" -solved_by = 1292 +solved_by = 1299 difficulty_rating = "40%" content = """ diff --git a/src/P366/problem.jl b/src/P366/problem.jl index f213f72..8adef96 100644 --- a/src/P366/problem.jl +++ b/src/P366/problem.jl @@ -3,7 +3,7 @@ module Problem366 title = "Problem 366: Stone Game III" published_on = "Saturday, 7th January 2012, 07:00 pm" -solved_by = 691 +solved_by = 695 difficulty_rating = "40%" content = """ Two players, Anton and Bernhard, are playing the following game. diff --git a/src/P367/problem.jl b/src/P367/problem.jl index aa16608..22f4903 100644 --- a/src/P367/problem.jl +++ b/src/P367/problem.jl @@ -3,7 +3,7 @@ module Problem367 title = "Problem 367: Bozo sort" published_on = "Saturday, 14th January 2012, 10:00 pm" -solved_by = 525 +solved_by = 529 difficulty_rating = "55%" content = """ \e[1mBozo sort,\e[0m not to be confused with the slightly less efficient \e[1mbogo sort,\e[0m consists out of checking if the input sequence is sorted diff --git a/src/P368/problem.jl b/src/P368/problem.jl index 1121d5a..ddf32a4 100644 --- a/src/P368/problem.jl +++ b/src/P368/problem.jl @@ -3,7 +3,7 @@ module Problem368 title = "Problem 368: A Kempner-like series" published_on = "Sunday, 22nd January 2012, 01:00 am" -solved_by = 562 +solved_by = 566 difficulty_rating = "45%" content = """ The diff --git a/src/P369/problem.jl b/src/P369/problem.jl index 7f9e956..4f77450 100644 --- a/src/P369/problem.jl +++ b/src/P369/problem.jl @@ -3,7 +3,7 @@ module Problem369 title = "Problem 369: Badugi" published_on = "Sunday, 29th January 2012, 04:00 am" -solved_by = 471 +solved_by = 473 difficulty_rating = "60%" content = """ In a standard 52 card deck of playing cards, a set of 4 cards is a \e[1mBadugi\e[0m if it contains 4 cards with no pairs and no two cards of diff --git a/src/P37/problem.jl b/src/P37/problem.jl index 1082f82..658aaec 100644 --- a/src/P37/problem.jl +++ b/src/P37/problem.jl @@ -3,7 +3,7 @@ module Problem37 title = "Problem 37: Truncatable primes" published_on = "Friday, 14th February 2003, 06:00 pm" -solved_by = 76391 +solved_by = 76515 difficulty_rating = "5%" content = """ The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, diff --git a/src/P370/problem.jl b/src/P370/problem.jl index 2dbdff5..e05e477 100644 --- a/src/P370/problem.jl +++ b/src/P370/problem.jl @@ -3,7 +3,7 @@ module Problem370 title = "Problem 370: Geometric triangles" published_on = "Sunday, 5th February 2012, 07:00 am" -solved_by = 531 +solved_by = 533 difficulty_rating = "65%" content = """ Let us define a geometric triangle as an integer sided triangle with sides a ≤ b ≤ c so that its sides form a \e[1mgeometric diff --git a/src/P371/problem.jl b/src/P371/problem.jl index 2aa035b..660e3cc 100644 --- a/src/P371/problem.jl +++ b/src/P371/problem.jl @@ -3,7 +3,7 @@ module Problem371 title = "Problem 371: Licence plates" published_on = "Sunday, 12th February 2012, 10:00 am" -solved_by = 1651 +solved_by = 1663 difficulty_rating = "30%" content = """ Oregon licence plates consist of three letters followed by a three digit number (each digit can be from [0..9]). diff --git a/src/P372/problem.jl b/src/P372/problem.jl index d8d3b2e..d442695 100644 --- a/src/P372/problem.jl +++ b/src/P372/problem.jl @@ -3,7 +3,7 @@ module Problem372 title = "Problem 372: Pencils of rays" published_on = "Saturday, 18th February 2012, 01:00 pm" -solved_by = 409 +solved_by = 411 difficulty_rating = "60%" content = """ diff --git a/src/P373/problem.jl b/src/P373/problem.jl index 5f4c103..9efa741 100644 --- a/src/P373/problem.jl +++ b/src/P373/problem.jl @@ -3,7 +3,7 @@ module Problem373 title = "Problem 373: Circumscribed Circles" published_on = "Saturday, 25th February 2012, 04:00 pm" -solved_by = 342 +solved_by = 348 difficulty_rating = "75%" content = """ Every triangle has a circumscribed circle that goes through the three vertices. Consider all integer sided triangles for which the diff --git a/src/P374/problem.jl b/src/P374/problem.jl index 7d80b1e..6fadab5 100644 --- a/src/P374/problem.jl +++ b/src/P374/problem.jl @@ -3,7 +3,7 @@ module Problem374 title = "Problem 374: Maximum Integer Partition Product" published_on = "Saturday, 3rd March 2012, 07:00 pm" -solved_by = 690 +solved_by = 697 difficulty_rating = "40%" content = """ An integer partition of a number n is a way of writing n as a sum of positive integers. diff --git a/src/P375/problem.jl b/src/P375/problem.jl index 356c957..c5bdc6b 100644 --- a/src/P375/problem.jl +++ b/src/P375/problem.jl @@ -3,7 +3,7 @@ module Problem375 title = "Problem 375: Minimum of subsequences" published_on = "Saturday, 10th March 2012, 10:00 pm" -solved_by = 900 +solved_by = 906 difficulty_rating = "40%" content = """ Let Sₙ be an integer sequence produced with the following pseudo-random number generator: diff --git a/src/P376/problem.jl b/src/P376/problem.jl index 51de254..b462e21 100644 --- a/src/P376/problem.jl +++ b/src/P376/problem.jl @@ -3,7 +3,7 @@ module Problem376 title = "Problem 376: Nontransitive sets of dice" published_on = "Sunday, 18th March 2012, 01:00 am" -solved_by = 282 +solved_by = 284 difficulty_rating = "70%" content = """ Consider the following set of dice with nonstandard pips: diff --git a/src/P377/problem.jl b/src/P377/problem.jl index b7861a4..f008f54 100644 --- a/src/P377/problem.jl +++ b/src/P377/problem.jl @@ -3,7 +3,7 @@ module Problem377 title = "Problem 377: Sum of digits - experience #13" published_on = "Sunday, 25th March 2012, 05:00 am" -solved_by = 729 +solved_by = 734 difficulty_rating = "45%" content = """ diff --git a/src/P378/problem.jl b/src/P378/problem.jl index d54023a..15c8659 100644 --- a/src/P378/problem.jl +++ b/src/P378/problem.jl @@ -3,7 +3,7 @@ module Problem378 title = "Problem 378: Triangle Triples" published_on = "Sunday, 1st April 2012, 07:00 am" -solved_by = 882 +solved_by = 888 difficulty_rating = "35%" content = """ Let T(n) be the n diff --git a/src/P38/problem.jl b/src/P38/problem.jl index f9d0e7c..c3dc960 100644 --- a/src/P38/problem.jl +++ b/src/P38/problem.jl @@ -3,7 +3,7 @@ module Problem38 title = "Problem 38: Pandigital multiples" published_on = "Friday, 28th February 2003, 06:00 pm" -solved_by = 65570 +solved_by = 65661 difficulty_rating = "5%" content = """ Take the number 192 and multiply it by each of 1, 2, and 3: diff --git a/src/P380/problem.jl b/src/P380/problem.jl index 9dd227b..1b5eda0 100644 --- a/src/P380/problem.jl +++ b/src/P380/problem.jl @@ -3,7 +3,7 @@ module Problem380 title = "Problem 380: Amazing Mazes!" published_on = "Saturday, 14th April 2012, 02:00 pm" -solved_by = 523 +solved_by = 525 difficulty_rating = "60%" content = """ diff --git a/src/P381/problem.jl b/src/P381/problem.jl index 9bcfe6a..9dc7f4c 100644 --- a/src/P381/problem.jl +++ b/src/P381/problem.jl @@ -3,7 +3,7 @@ module Problem381 title = "Problem 381: (prime-k) factorial" published_on = "Saturday, 21st April 2012, 05:00 pm" -solved_by = 4326 +solved_by = 4348 difficulty_rating = "15%" content = """ For a prime p let S(p) = (∑ (p-k)!) mod(p) for 1 ≤ k ≤ 5. diff --git a/src/P382/problem.jl b/src/P382/problem.jl index b150a81..abf477f 100644 --- a/src/P382/problem.jl +++ b/src/P382/problem.jl @@ -3,7 +3,7 @@ module Problem382 title = "Problem 382: Generating polygons" published_on = "Saturday, 28th April 2012, 08:00 pm" -solved_by = 340 +solved_by = 341 difficulty_rating = "60%" content = """ A \e[1mpolygon\e[0m is a flat shape consisting of straight line segments that are joined to form a closed chain or circuit. A polygon diff --git a/src/P383/problem.jl b/src/P383/problem.jl index 075b7e4..543d91d 100644 --- a/src/P383/problem.jl +++ b/src/P383/problem.jl @@ -3,7 +3,7 @@ module Problem383 title = "Problem 383: Divisibility comparison between factorials" published_on = "Saturday, 5th May 2012, 11:00 pm" -solved_by = 482 +solved_by = 488 difficulty_rating = "50%" content = """ Let f₅(n) be the largest integer x for which 5ˣ divides n. diff --git a/src/P384/problem.jl b/src/P384/problem.jl index c9f2077..41edb2f 100644 --- a/src/P384/problem.jl +++ b/src/P384/problem.jl @@ -3,7 +3,7 @@ module Problem384 title = "Problem 384: Rudin-Shapiro sequence" published_on = "Sunday, 13th May 2012, 02:00 am" -solved_by = 334 +solved_by = 335 difficulty_rating = "65%" content = """ Define the sequence a(n) as the number of adjacent pairs of ones in the binary expansion of n (possibly overlapping). diff --git a/src/P385/problem.jl b/src/P385/problem.jl index a57694e..e56deb5 100644 --- a/src/P385/problem.jl +++ b/src/P385/problem.jl @@ -3,7 +3,7 @@ module Problem385 title = "Problem 385: Ellipses inside triangles" published_on = "Sunday, 20th May 2012, 05:00 am" -solved_by = 283 +solved_by = 284 difficulty_rating = "70%" content = """ diff --git a/src/P386/problem.jl b/src/P386/problem.jl index 209221b..4644cd3 100644 --- a/src/P386/problem.jl +++ b/src/P386/problem.jl @@ -3,7 +3,7 @@ module Problem386 title = "Problem 386: Maximum length of an antichain" published_on = "Sunday, 27th May 2012, 08:00 am" -solved_by = 742 +solved_by = 744 difficulty_rating = "40%" content = """ Let n be an integer and S(n) be the set of factors of n. diff --git a/src/P387/problem.jl b/src/P387/problem.jl index 688c727..f9e73d3 100644 --- a/src/P387/problem.jl +++ b/src/P387/problem.jl @@ -3,7 +3,7 @@ module Problem387 title = "Problem 387: Harshad Numbers" published_on = "Sunday, 3rd June 2012, 11:00 am" -solved_by = 4792 +solved_by = 4818 difficulty_rating = "10%" content = """ A \e[1mHarshad or Niven number\e[0m is a number that is divisible by the sum of its digits. diff --git a/src/P388/problem.jl b/src/P388/problem.jl index 2d9816a..52171d5 100644 --- a/src/P388/problem.jl +++ b/src/P388/problem.jl @@ -3,7 +3,7 @@ module Problem388 title = "Problem 388: Distinct Lines" published_on = "Saturday, 9th June 2012, 02:00 pm" -solved_by = 588 +solved_by = 592 difficulty_rating = "55%" content = """ Consider all lattice points (a,b,c) with 0 ≤ a,b,c ≤ N. diff --git a/src/P389/problem.jl b/src/P389/problem.jl index b0d9fa0..ca0e4d8 100644 --- a/src/P389/problem.jl +++ b/src/P389/problem.jl @@ -3,7 +3,7 @@ module Problem389 title = "Problem 389: Platonic Dice" published_on = "Saturday, 16th June 2012, 05:00 pm" -solved_by = 1560 +solved_by = 1566 difficulty_rating = "30%" content = """ An unbiased single 4-sided die is thrown and its value, T, is noted. diff --git a/src/P39/problem.jl b/src/P39/problem.jl index 2fc373c..7575599 100644 --- a/src/P39/problem.jl +++ b/src/P39/problem.jl @@ -3,7 +3,7 @@ module Problem39 title = "Problem 39: Integer right triangles" published_on = "Friday, 14th March 2003, 06:00 pm" -solved_by = 75978 +solved_by = 76085 difficulty_rating = "5%" content = """ If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120. diff --git a/src/P390/problem.jl b/src/P390/problem.jl index df9a250..ab17b3f 100644 --- a/src/P390/problem.jl +++ b/src/P390/problem.jl @@ -3,7 +3,7 @@ module Problem390 title = "Problem 390: Triangles with non rational sides and integral area" published_on = "Saturday, 23rd June 2012, 08:00 pm" -solved_by = 575 +solved_by = 577 difficulty_rating = "60%" content = """ Consider the triangle with sides \\sqrt 5, \\sqrt {65} and \\sqrt {68}. diff --git a/src/P392/problem.jl b/src/P392/problem.jl index 3d6d2da..afe948d 100644 --- a/src/P392/problem.jl +++ b/src/P392/problem.jl @@ -3,7 +3,7 @@ module Problem392 title = "Problem 392: Enmeshed unit circle" published_on = "Saturday, 1st September 2012, 02:00 pm" -solved_by = 795 +solved_by = 798 difficulty_rating = "35%" content = """ diff --git a/src/P393/problem.jl b/src/P393/problem.jl index 7c500e7..b1a004a 100644 --- a/src/P393/problem.jl +++ b/src/P393/problem.jl @@ -3,7 +3,7 @@ module Problem393 title = "Problem 393: Migrating ants" published_on = "Saturday, 8th September 2012, 05:00 pm" -solved_by = 784 +solved_by = 789 difficulty_rating = "50%" content = """ An n×n grid of squares contains n² ants, one ant per square. diff --git a/src/P394/problem.jl b/src/P394/problem.jl index eb14dbd..97d52b9 100644 --- a/src/P394/problem.jl +++ b/src/P394/problem.jl @@ -3,7 +3,7 @@ module Problem394 title = "Problem 394: Eating pie" published_on = "Saturday, 15th September 2012, 08:00 pm" -solved_by = 540 +solved_by = 544 difficulty_rating = "55%" content = """ diff --git a/src/P395/problem.jl b/src/P395/problem.jl index 55e2e72..cfbacb1 100644 --- a/src/P395/problem.jl +++ b/src/P395/problem.jl @@ -3,7 +3,7 @@ module Problem395 title = "Problem 395: Pythagorean tree" published_on = "Saturday, 22nd September 2012, 11:00 pm" -solved_by = 707 +solved_by = 711 difficulty_rating = "40%" content = """ diff --git a/src/P396/problem.jl b/src/P396/problem.jl index 6e5d033..f89d332 100644 --- a/src/P396/problem.jl +++ b/src/P396/problem.jl @@ -3,7 +3,7 @@ module Problem396 title = "Problem 396: Weak Goodstein sequence" published_on = "Sunday, 30th September 2012, 02:00 am" -solved_by = 673 +solved_by = 675 difficulty_rating = "40%" content = """ For any positive integer n, the \e[1mnth weak Goodstein sequence\e[0m {g₁, g₂, g₃, ...} is defined as: diff --git a/src/P397/problem.jl b/src/P397/problem.jl index 215e36a..baa79ce 100644 --- a/src/P397/problem.jl +++ b/src/P397/problem.jl @@ -3,7 +3,7 @@ module Problem397 title = "Problem 397: Triangle on parabola" published_on = "Sunday, 7th October 2012, 05:00 am" -solved_by = 272 +solved_by = 273 difficulty_rating = "70%" content = """ On the parabola y = x²/k, three points A(a, a²/k), B(b, b²/k) and C(c, c²/k) are chosen. diff --git a/src/P398/problem.jl b/src/P398/problem.jl index 08e92d2..67f0cd2 100644 --- a/src/P398/problem.jl +++ b/src/P398/problem.jl @@ -3,7 +3,7 @@ module Problem398 title = "Problem 398: Cutting rope" published_on = "Sunday, 14th October 2012, 08:00 am" -solved_by = 385 +solved_by = 388 difficulty_rating = "55%" content = """ Inside a rope of length n, n-1 points are placed with distance 1 from each other and from the endpoints. Among these points, diff --git a/src/P399/problem.jl b/src/P399/problem.jl index 6e7dcce..dc8b431 100644 --- a/src/P399/problem.jl +++ b/src/P399/problem.jl @@ -3,7 +3,7 @@ module Problem399 title = "Problem 399: Squarefree Fibonacci Numbers" published_on = "Sunday, 21st October 2012, 11:00 am" -solved_by = 576 +solved_by = 579 difficulty_rating = "45%" content = """ The first 15 fibonacci numbers are: diff --git a/src/P4/problem.jl b/src/P4/problem.jl index c63d289..14dea4a 100644 --- a/src/P4/problem.jl +++ b/src/P4/problem.jl @@ -3,7 +3,7 @@ module Problem4 title = "Problem 4: Largest palindrome product" published_on = "Friday, 16th November 2001, 06:00 pm" -solved_by = 493978 +solved_by = 494195 difficulty_rating = "5%" content = """ A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is diff --git a/src/P40/problem.jl b/src/P40/problem.jl index cdcf454..f04e3f3 100644 --- a/src/P40/problem.jl +++ b/src/P40/problem.jl @@ -3,7 +3,7 @@ module Problem40 title = "Problem 40: Champernowne's constant" published_on = "Friday, 28th March 2003, 06:00 pm" -solved_by = 82991 +solved_by = 83113 difficulty_rating = "5%" content = """ An irrational decimal fraction is created by concatenating the positive integers: diff --git a/src/P400/problem.jl b/src/P400/problem.jl index 1a3548e..ad4e9a4 100644 --- a/src/P400/problem.jl +++ b/src/P400/problem.jl @@ -3,7 +3,7 @@ module Problem400 title = "Problem 400: Fibonacci tree game" published_on = "Saturday, 27th October 2012, 02:00 pm" -solved_by = 477 +solved_by = 480 difficulty_rating = "55%" content = """ diff --git a/src/P401/problem.jl b/src/P401/problem.jl index 9f34805..47c459c 100644 --- a/src/P401/problem.jl +++ b/src/P401/problem.jl @@ -3,7 +3,7 @@ module Problem401 title = "Problem 401: Sum of squares of divisors" published_on = "Saturday, 10th November 2012, 04:00 pm" -solved_by = 2607 +solved_by = 2616 difficulty_rating = "25%" content = """ The divisors of 6 are 1,2,3 and 6. diff --git a/src/P402/problem.jl b/src/P402/problem.jl index b9dfdf9..7c2fc02 100644 --- a/src/P402/problem.jl +++ b/src/P402/problem.jl @@ -3,7 +3,7 @@ module Problem402 title = "Problem 402: Integer-valued polynomials" published_on = "Saturday, 17th November 2012, 07:00 pm" -solved_by = 414 +solved_by = 417 difficulty_rating = "55%" content = """ It can be shown that the polynomial n⁴ + 4n³ + 2n² + 5n is a multiple of 6 for every integer n. It can also be shown that 6 is the diff --git a/src/P403/problem.jl b/src/P403/problem.jl index 473dbf0..102a4a8 100644 --- a/src/P403/problem.jl +++ b/src/P403/problem.jl @@ -3,7 +3,7 @@ module Problem403 title = "Problem 403: Lattice points enclosed by parabola and line" published_on = "Saturday, 24th November 2012, 10:00 pm" -solved_by = 361 +solved_by = 362 difficulty_rating = "55%" content = """ For integers a and b, we define D(a, b) as the domain enclosed by the parabola y = x² and the line y = a·x + b: diff --git a/src/P404/problem.jl b/src/P404/problem.jl index d26789d..0ef9c49 100644 --- a/src/P404/problem.jl +++ b/src/P404/problem.jl @@ -3,7 +3,7 @@ module Problem404 title = "Problem 404: Crisscross Ellipses" published_on = "Sunday, 2nd December 2012, 01:00 am" -solved_by = 324 +solved_by = 326 difficulty_rating = "60%" content = """ diff --git a/src/P405/problem.jl b/src/P405/problem.jl index 2993ca7..b0bd4aa 100644 --- a/src/P405/problem.jl +++ b/src/P405/problem.jl @@ -3,7 +3,7 @@ module Problem405 title = "Problem 405 A: rectangular tiling" published_on = "Sunday, 9th December 2012, 04:00 am" -solved_by = 618 +solved_by = 622 difficulty_rating = "40%" content = """ diff --git a/src/P406/problem.jl b/src/P406/problem.jl index 1977e80..130e2ec 100644 --- a/src/P406/problem.jl +++ b/src/P406/problem.jl @@ -3,7 +3,7 @@ module Problem406 title = "Problem 406: Guessing Game" published_on = "Sunday, 16th December 2012, 07:00 am" -solved_by = 377 +solved_by = 379 difficulty_rating = "50%" content = """ We are trying to find a hidden number selected from the set of integers {1, 2, ..., diff --git a/src/P407/problem.jl b/src/P407/problem.jl index 87a1b21..88e75e4 100644 --- a/src/P407/problem.jl +++ b/src/P407/problem.jl @@ -3,7 +3,7 @@ module Problem407 title = "Problem 407: Idempotents" published_on = "Sunday, 23rd December 2012, 10:00 am" -solved_by = 2500 +solved_by = 2507 difficulty_rating = "20%" content = """ If we calculate a² mod 6 for 0 ≤ a ≤ 5 we get: 0,1,4,3,4,1. diff --git a/src/P408/problem.jl b/src/P408/problem.jl index c5454af..28cdf41 100644 --- a/src/P408/problem.jl +++ b/src/P408/problem.jl @@ -3,7 +3,7 @@ module Problem408 title = "Problem 408: Admissible paths through a grid" published_on = "Saturday, 29th December 2012, 01:00 pm" -solved_by = 575 +solved_by = 578 difficulty_rating = "50%" content = """ Let's call a lattice point (x, y) inadmissible if x, y and x + y are all positive perfect squares. diff --git a/src/P409/problem.jl b/src/P409/problem.jl index 8cd7df5..2c11a8b 100644 --- a/src/P409/problem.jl +++ b/src/P409/problem.jl @@ -3,7 +3,7 @@ module Problem409 title = "Problem 409: Nim Extreme" published_on = "Saturday, 5th January 2013, 04:00 pm" -solved_by = 454 +solved_by = 458 difficulty_rating = "55%" content = """ Let n be a positive integer. Consider nim positions where: diff --git a/src/P41/problem.jl b/src/P41/problem.jl index c039531..781dc73 100644 --- a/src/P41/problem.jl +++ b/src/P41/problem.jl @@ -3,7 +3,7 @@ module Problem41 title = "Problem 41: Pandigital prime" published_on = "Friday, 11th April 2003, 06:00 pm" -solved_by = 70798 +solved_by = 70902 difficulty_rating = "5%" content = """ We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4- diff --git a/src/P410/problem.jl b/src/P410/problem.jl index 8f47bd6..d1ffbcf 100644 --- a/src/P410/problem.jl +++ b/src/P410/problem.jl @@ -3,7 +3,7 @@ module Problem410 title = "Problem 410: Circle and tangent line" published_on = "Saturday, 12th January 2013, 07:00 pm" -solved_by = 279 +solved_by = 280 difficulty_rating = "70%" content = """ Let C be the circle with radius r, x² + y² = r². We choose two points P(a, b) and Q(-a, c) so that the line passing through P and diff --git a/src/P411/problem.jl b/src/P411/problem.jl index 5475b1d..13a5bb6 100644 --- a/src/P411/problem.jl +++ b/src/P411/problem.jl @@ -3,7 +3,7 @@ module Problem411 title = "Problem 411: Uphill paths" published_on = "Saturday, 19th January 2013, 10:00 pm" -solved_by = 661 +solved_by = 670 difficulty_rating = "45%" content = """ diff --git a/src/P412/problem.jl b/src/P412/problem.jl index 69b4384..ee63285 100644 --- a/src/P412/problem.jl +++ b/src/P412/problem.jl @@ -3,7 +3,7 @@ module Problem412 title = "Problem 412: Gnomon numbering" published_on = "Sunday, 27th January 2013, 01:00 am" -solved_by = 501 +solved_by = 506 difficulty_rating = "50%" content = """ For integers m, n (0 ≤ n < m), let L(m, n) be an m×m grid with the top-right n×n grid removed. diff --git a/src/P414/problem.jl b/src/P414/problem.jl index 5461d34..727f48d 100644 --- a/src/P414/problem.jl +++ b/src/P414/problem.jl @@ -3,7 +3,7 @@ module Problem414 title = "Problem 414: Kaprekar constant" published_on = "Sunday, 10th February 2013, 07:00 am" -solved_by = 284 +solved_by = 286 difficulty_rating = "60%" content = """ 6174 is a remarkable number; if we sort its digits in increasing order and subtract that number from the number you get when diff --git a/src/P415/problem.jl b/src/P415/problem.jl index 77caf35..c6d4c51 100644 --- a/src/P415/problem.jl +++ b/src/P415/problem.jl @@ -3,7 +3,7 @@ module Problem415 title = "Problem 415: Titanic sets" published_on = "Sunday, 17th February 2013, 10:00 am" -solved_by = 312 +solved_by = 313 difficulty_rating = "100%" content = """ A set of lattice points S is called a titanic set if there exists a line passing through exactly two points in S. diff --git a/src/P416/problem.jl b/src/P416/problem.jl index df6feb9..77d5b9f 100644 --- a/src/P416/problem.jl +++ b/src/P416/problem.jl @@ -3,7 +3,7 @@ module Problem416 title = "Problem 416: A frog's trip" published_on = "Saturday, 23rd February 2013, 01:00 pm" -solved_by = 293 +solved_by = 294 difficulty_rating = "85%" content = """ A row of n squares contains a frog in the leftmost square. By successive jumps the frog goes to the rightmost square and then diff --git a/src/P417/problem.jl b/src/P417/problem.jl index 9eeb8a8..9542907 100644 --- a/src/P417/problem.jl +++ b/src/P417/problem.jl @@ -3,7 +3,7 @@ module Problem417 title = "Problem 417: Reciprocal cycles II" published_on = "Saturday, 2nd March 2013, 04:00 pm" -solved_by = 886 +solved_by = 894 difficulty_rating = "35%" content = """ A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given: diff --git a/src/P418/problem.jl b/src/P418/problem.jl index 5b0f237..de246ea 100644 --- a/src/P418/problem.jl +++ b/src/P418/problem.jl @@ -3,7 +3,7 @@ module Problem418 title = "Problem 418: Factorisation triples" published_on = "Saturday, 9th March 2013, 07:00 pm" -solved_by = 698 +solved_by = 700 difficulty_rating = "40%" content = """ Let n be a positive integer. An integer triple (a, b, c) is called a factorisation triple of n if: diff --git a/src/P419/problem.jl b/src/P419/problem.jl index db15f53..be26f01 100644 --- a/src/P419/problem.jl +++ b/src/P419/problem.jl @@ -3,7 +3,7 @@ module Problem419 title = "Problem 419: Look and say sequence" published_on = "Saturday, 16th March 2013, 10:00 pm" -solved_by = 495 +solved_by = 498 difficulty_rating = "50%" content = """ The \e[1mlook and say\e[0m sequence goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ... diff --git a/src/P42/problem.jl b/src/P42/problem.jl index b570028..a458832 100644 --- a/src/P42/problem.jl +++ b/src/P42/problem.jl @@ -3,7 +3,7 @@ module Problem42 title = "Problem 42: Coded triangle numbers" published_on = "Friday, 25th April 2003, 06:00 pm" -solved_by = 77100 +solved_by = 77205 difficulty_rating = "5%" content = """ The nᵗʰ term of the sequence of triangle numbers is given by, tₙ = ½n(n+1); so the first ten triangle numbers are: diff --git a/src/P420/problem.jl b/src/P420/problem.jl index 3bf55c3..0a11c17 100644 --- a/src/P420/problem.jl +++ b/src/P420/problem.jl @@ -3,7 +3,7 @@ module Problem420 title = "Problem 420: 2x2 positive integer matrix" published_on = "Sunday, 24th March 2013, 01:00 am" -solved_by = 441 +solved_by = 446 difficulty_rating = "60%" content = """ A diff --git a/src/P421/problem.jl b/src/P421/problem.jl index db824a7..568855a 100644 --- a/src/P421/problem.jl +++ b/src/P421/problem.jl @@ -3,7 +3,7 @@ module Problem421 title = "Problem 421: Prime factors of n¹⁵+1" published_on = "Sunday, 31st March 2013, 04:00 am" -solved_by = 659 +solved_by = 665 difficulty_rating = "50%" content = """ Numbers of the form n¹⁵+1 are composite for every integer n > 1. diff --git a/src/P422/problem.jl b/src/P422/problem.jl index 2ae8a7c..0e24f19 100644 --- a/src/P422/problem.jl +++ b/src/P422/problem.jl @@ -3,7 +3,7 @@ module Problem422 title = "Problem 422: Sequence of points on a hyperbola" published_on = "Sunday, 7th April 2013, 07:00 am" -solved_by = 277 +solved_by = 278 difficulty_rating = "75%" content = """ Let H be the hyperbola defined by the equation 12 diff --git a/src/P423/problem.jl b/src/P423/problem.jl index 61b70b3..5913213 100644 --- a/src/P423/problem.jl +++ b/src/P423/problem.jl @@ -3,7 +3,7 @@ module Problem423 title = "Problem 423: Consecutive die throws" published_on = "Sunday, 14th April 2013, 10:00 am" -solved_by = 492 +solved_by = 496 difficulty_rating = "45%" content = """ Let n be a positive integer. diff --git a/src/P424/problem.jl b/src/P424/problem.jl index 3d0f089..73c1ff6 100644 --- a/src/P424/problem.jl +++ b/src/P424/problem.jl @@ -3,7 +3,7 @@ module Problem424 title = "Problem 424: Kakuro" published_on = "Saturday, 20th April 2013, 01:00 pm" -solved_by = 416 +solved_by = 419 difficulty_rating = "60%" content = """ The above is an example of a cryptic kakuro (also known as cross sums, or even sums cross) puzzle, with its final solution on the right. (The common rules of kakuro puzzles can be found easily on numerous internet sites. Other related information can also be currently found at diff --git a/src/P425/problem.jl b/src/P425/problem.jl index 3ade5fd..5f65eef 100644 --- a/src/P425/problem.jl +++ b/src/P425/problem.jl @@ -3,7 +3,7 @@ module Problem425 title = "Problem 425: Prime connection" published_on = "Saturday, 27th April 2013, 04:00 pm" -solved_by = 1495 +solved_by = 1504 difficulty_rating = "25%" content = """ Two positive numbers A and B are said to be connected (denoted by "A ↔ B") if one of these conditions holds: diff --git a/src/P426/problem.jl b/src/P426/problem.jl index 3898c5f..ce995e8 100644 --- a/src/P426/problem.jl +++ b/src/P426/problem.jl @@ -3,7 +3,7 @@ module Problem426 title = "Problem 426: Box-ball system" published_on = "Saturday, 4th May 2013, 07:00 pm" -solved_by = 254 +solved_by = 255 difficulty_rating = "75%" content = """ diff --git a/src/P428/problem.jl b/src/P428/problem.jl index ad4b89b..c66411d 100644 --- a/src/P428/problem.jl +++ b/src/P428/problem.jl @@ -3,7 +3,7 @@ module Problem428 title = "Problem 428: Necklace of circles" published_on = "Sunday, 19th May 2013, 01:00 am" -solved_by = 246 +solved_by = 248 difficulty_rating = "90%" content = """ Let diff --git a/src/P429/problem.jl b/src/P429/problem.jl index e8e1230..4a16e90 100644 --- a/src/P429/problem.jl +++ b/src/P429/problem.jl @@ -3,7 +3,7 @@ module Problem429 title = "Problem 429: Sum of squares of unitary divisors" published_on = "Sunday, 26th May 2013, 04:00 am" -solved_by = 2575 +solved_by = 2590 difficulty_rating = "20%" content = """ A unitary divisor d of a number n is a divisor of n that has the property gcd(d, n/d) = 1. diff --git a/src/P43/problem.jl b/src/P43/problem.jl index 4f9cfbb..ba3d68b 100644 --- a/src/P43/problem.jl +++ b/src/P43/problem.jl @@ -3,7 +3,7 @@ module Problem43 title = "Problem 43: Sub-string divisibility" published_on = "Friday, 9th May 2003, 06:00 pm" -solved_by = 62318 +solved_by = 62417 difficulty_rating = "5%" content = """ The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it diff --git a/src/P430/problem.jl b/src/P430/problem.jl index 8d3292e..7435562 100644 --- a/src/P430/problem.jl +++ b/src/P430/problem.jl @@ -3,7 +3,7 @@ module Problem430 title = "Problem 430: Range flips" published_on = "Sunday, 2nd June 2013, 07:00 am" -solved_by = 872 +solved_by = 873 difficulty_rating = "35%" content = """ N diff --git a/src/P431/problem.jl b/src/P431/problem.jl index 19adb04..b91d352 100644 --- a/src/P431/problem.jl +++ b/src/P431/problem.jl @@ -3,7 +3,7 @@ module Problem431 title = "Problem 431: Square Space Silo" published_on = "Sunday, 9th June 2013, 10:00 am" -solved_by = 629 +solved_by = 633 difficulty_rating = "40%" content = """ Fred the farmer arranges to have a new storage silo installed on his farm and having an obsession for all things square he is absolutely devastated when he discovers that it is circular. Quentin, the representative from the company that installed the silo, explains that they only manufacture cylindrical silos, but he points out that it is resting on a square base. Fred is not amused and insists that it is removed from his property. diff --git a/src/P432/problem.jl b/src/P432/problem.jl index f00168c..968bdde 100644 --- a/src/P432/problem.jl +++ b/src/P432/problem.jl @@ -3,7 +3,7 @@ module Problem432 title = "Problem 432: Totient sum" published_on = "Saturday, 15th June 2013, 01:00 pm" -solved_by = 493 +solved_by = 497 difficulty_rating = "70%" content = """ Let S(n,m) = ∑φ(n × i) for 1 ≤ i ≤ m. (φ is Euler's totient function) diff --git a/src/P434/problem.jl b/src/P434/problem.jl index 01736f9..0f7980d 100644 --- a/src/P434/problem.jl +++ b/src/P434/problem.jl @@ -3,7 +3,7 @@ module Problem434 title = "Problem 434: Rigid graphs" published_on = "Saturday, 29th June 2013, 07:00 pm" -solved_by = 340 +solved_by = 341 difficulty_rating = "75%" content = """ Recall that a graph is a collection of vertices and edges connecting the vertices, and that two vertices connected by an edge are called adjacent. diff --git a/src/P435/problem.jl b/src/P435/problem.jl index 0c983f6..53a198b 100644 --- a/src/P435/problem.jl +++ b/src/P435/problem.jl @@ -3,7 +3,7 @@ module Problem435 title = "Problem 435: Polynomials of Fibonacci numbers" published_on = "Saturday, 7th September 2013, 04:00 pm" -solved_by = 1140 +solved_by = 1143 difficulty_rating = "30%" content = """ The diff --git a/src/P436/problem.jl b/src/P436/problem.jl index 88cb3ba..f3e6e49 100644 --- a/src/P436/problem.jl +++ b/src/P436/problem.jl @@ -3,7 +3,7 @@ module Problem436 title = "Problem 436: Unfair wager" published_on = "Saturday, 14th September 2013, 07:00 pm" -solved_by = 460 +solved_by = 466 difficulty_rating = "55%" content = """ Julie proposes the following wager to her sister Louise. diff --git a/src/P437/problem.jl b/src/P437/problem.jl index e15cb02..3cd25eb 100644 --- a/src/P437/problem.jl +++ b/src/P437/problem.jl @@ -3,7 +3,7 @@ module Problem437 title = "Problem 437: Fibonacci primitive roots" published_on = "Saturday, 21st September 2013, 10:00 pm" -solved_by = 805 +solved_by = 810 difficulty_rating = "35%" content = """ When we calculate 8ⁿ modulo 11 for n=0 to 9 we get: 1, 8, 9, 6, 4, 10, 3, 2, 5, 7. diff --git a/src/P438/problem.jl b/src/P438/problem.jl index 170da62..f403df4 100644 --- a/src/P438/problem.jl +++ b/src/P438/problem.jl @@ -3,7 +3,7 @@ module Problem438 title = "Problem 438: Integer part of polynomial equation's solutions" published_on = "Sunday, 29th September 2013, 01:00 am" -solved_by = 278 +solved_by = 279 difficulty_rating = "95%" content = """ For an n-tuple of integers t = (a₁, ..., aₙ), let (x₁, ..., xₙ) be the solutions of the polynomial equation xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ = 0. diff --git a/src/P44/problem.jl b/src/P44/problem.jl index 0c1e9ca..0aa2d1f 100644 --- a/src/P44/problem.jl +++ b/src/P44/problem.jl @@ -3,7 +3,7 @@ module Problem44 title = "Problem 44: Pentagon numbers" published_on = "Friday, 23rd May 2003, 06:00 pm" -solved_by = 60998 +solved_by = 61088 difficulty_rating = "5%" content = """ Pentagonal numbers are generated by the formula, Pₙ=n(3n-1)/2. The first ten pentagonal numbers are: diff --git a/src/P440/problem.jl b/src/P440/problem.jl index 69056a3..1f807f2 100644 --- a/src/P440/problem.jl +++ b/src/P440/problem.jl @@ -3,7 +3,7 @@ module Problem440 title = "Problem 440: GCD and Tiling" published_on = "Sunday, 13th October 2013, 07:00 am" -solved_by = 380 +solved_by = 381 difficulty_rating = "60%" content = """ We want to tile a board of length n and height 1 completely, with either 1 × 2 blocks or 1 × 1 blocks with a single decimal digit diff --git a/src/P441/problem.jl b/src/P441/problem.jl index dad3e4d..3549b5d 100644 --- a/src/P441/problem.jl +++ b/src/P441/problem.jl @@ -3,7 +3,7 @@ module Problem441 title = "Problem 441: The inverse summation of coprime couples" published_on = "Sunday, 20th October 2013, 10:00 am" -solved_by = 359 +solved_by = 360 difficulty_rating = "65%" content = """ For an integer M, we define R(M) as the sum of 1/(p·q) for all the integer pairs p and q which satisfy all of these conditions: diff --git a/src/P442/problem.jl b/src/P442/problem.jl index d685f58..a59ef5d 100644 --- a/src/P442/problem.jl +++ b/src/P442/problem.jl @@ -3,7 +3,7 @@ module Problem442 title = "Problem 442: Eleven-free integers" published_on = "Saturday, 26th October 2013, 01:00 pm" -solved_by = 398 +solved_by = 399 difficulty_rating = "60%" content = """ An integer is called eleven-free if its decimal expansion does not contain any substring representing a power of 11 except 1. diff --git a/src/P443/problem.jl b/src/P443/problem.jl index 526b3f4..8b71c44 100644 --- a/src/P443/problem.jl +++ b/src/P443/problem.jl @@ -3,7 +3,7 @@ module Problem443 title = "Problem 443: GCD sequence" published_on = "Saturday, 2nd November 2013, 04:00 pm" -solved_by = 1145 +solved_by = 1154 difficulty_rating = "30%" content = """ Let g(n) be a sequence defined as follows: diff --git a/src/P444/problem.jl b/src/P444/problem.jl index 9a8f3aa..2781565 100644 --- a/src/P444/problem.jl +++ b/src/P444/problem.jl @@ -3,7 +3,7 @@ module Problem444 title = "Problem 444: The Roundtable Lottery" published_on = "Saturday, 9th November 2013, 07:00 pm" -solved_by = 307 +solved_by = 309 difficulty_rating = "60%" content = """ A group of p people decide to sit down at a round table and play a lottery-ticket trading game. Each person starts off with a randomly-assigned, unscratched lottery ticket. Each ticket, when scratched, reveals a whole-pound prize ranging anywhere from £1 to £p, with no two tickets alike. The goal of the game is for all of the players to maximize the winnings of the ticket they hold upon leaving the game. diff --git a/src/P445/problem.jl b/src/P445/problem.jl index dcaf82a..7540cd2 100644 --- a/src/P445/problem.jl +++ b/src/P445/problem.jl @@ -3,7 +3,7 @@ module Problem445 title = "Problem 445: Retractions A" published_on = "Saturday, 16th November 2013, 10:00 pm" -solved_by = 383 +solved_by = 384 difficulty_rating = "50%" content = """ diff --git a/src/P447/problem.jl b/src/P447/problem.jl index 54607df..3de6610 100644 --- a/src/P447/problem.jl +++ b/src/P447/problem.jl @@ -3,7 +3,7 @@ module Problem447 title = "Problem 447: Retractions C" published_on = "Saturday, 16th November 2013, 10:00 pm" -solved_by = 295 +solved_by = 297 difficulty_rating = "95%" content = """ diff --git a/src/P448/problem.jl b/src/P448/problem.jl index cde3bd8..8854036 100644 --- a/src/P448/problem.jl +++ b/src/P448/problem.jl @@ -3,7 +3,7 @@ module Problem448 title = "Problem 448: Average least common multiple" published_on = "Sunday, 24th November 2013, 01:00 am" -solved_by = 349 +solved_by = 351 difficulty_rating = "80%" content = """ The function \e[1mlcm\e[0m(a,b) denotes the least common multiple of a and b. diff --git a/src/P449/problem.jl b/src/P449/problem.jl index eadedfd..171f55b 100644 --- a/src/P449/problem.jl +++ b/src/P449/problem.jl @@ -3,7 +3,7 @@ module Problem449 title = "Problem 449: Chocolate covered candy" published_on = "Sunday, 8th December 2013, 04:00 am" -solved_by = 919 +solved_by = 926 difficulty_rating = "40%" content = """ Phil the confectioner is making a new batch of chocolate covered candy. Each candy centre is shaped like an ellipsoid of revolution defined by the equation: diff --git a/src/P45/problem.jl b/src/P45/problem.jl index 8f98bcb..68bf7a2 100644 --- a/src/P45/problem.jl +++ b/src/P45/problem.jl @@ -3,7 +3,7 @@ module Problem45 title = "Problem 45: Triangular, pentagonal, and hexagonal" published_on = "Friday, 6th June 2003, 06:00 pm" -solved_by = 73568 +solved_by = 73668 difficulty_rating = "5%" content = """ Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: diff --git a/src/P451/problem.jl b/src/P451/problem.jl index 13113f2..9070a37 100644 --- a/src/P451/problem.jl +++ b/src/P451/problem.jl @@ -3,7 +3,7 @@ module Problem451 title = "Problem 451: Modular inverses" published_on = "Sunday, 22nd December 2013, 10:00 am" -solved_by = 1460 +solved_by = 1463 difficulty_rating = "30%" content = """ Consider the number 15. diff --git a/src/P452/problem.jl b/src/P452/problem.jl index 97f36cc..5d545e4 100644 --- a/src/P452/problem.jl +++ b/src/P452/problem.jl @@ -3,7 +3,7 @@ module Problem452 title = "Problem 452: Long Products" published_on = "Saturday, 28th December 2013, 01:00 pm" -solved_by = 585 +solved_by = 589 difficulty_rating = "45%" content = """ Define F(m,n) as the number of n-tuples of positive integers for which the product of the elements doesn't exceed m. diff --git a/src/P454/problem.jl b/src/P454/problem.jl index 05856ce..596286c 100644 --- a/src/P454/problem.jl +++ b/src/P454/problem.jl @@ -3,7 +3,7 @@ module Problem454 title = "Problem 454: Diophantine reciprocals III" published_on = "Saturday, 11th January 2014, 07:00 pm" -solved_by = 474 +solved_by = 476 difficulty_rating = "50%" content = """ In the following equation diff --git a/src/P455/problem.jl b/src/P455/problem.jl index 7e676b4..d05751a 100644 --- a/src/P455/problem.jl +++ b/src/P455/problem.jl @@ -3,7 +3,7 @@ module Problem455 title = "Problem 455: Powers With Trailing Digits" published_on = "Saturday, 18th January 2014, 10:00 pm" -solved_by = 724 +solved_by = 727 difficulty_rating = "40%" content = """ Let f(n) be the largest positive integer x less than 10⁹ such that the last 9 digits of nˣ form the number x (including leading diff --git a/src/P456/problem.jl b/src/P456/problem.jl index 7aca196..d98ce78 100644 --- a/src/P456/problem.jl +++ b/src/P456/problem.jl @@ -3,7 +3,7 @@ module Problem456 title = "Problem 456: Triangles containing the origin II" published_on = "Sunday, 26th January 2014, 01:00 am" -solved_by = 402 +solved_by = 404 difficulty_rating = "55%" content = """ Define: diff --git a/src/P457/problem.jl b/src/P457/problem.jl index f208798..4341092 100644 --- a/src/P457/problem.jl +++ b/src/P457/problem.jl @@ -3,7 +3,7 @@ module Problem457 title = "Problem 457: A polynomial modulo the square of a prime" published_on = "Sunday, 2nd February 2014, 04:00 am" -solved_by = 806 +solved_by = 813 difficulty_rating = "35%" content = """ Let f(n) = n² - 3n - 1. diff --git a/src/P458/problem.jl b/src/P458/problem.jl index a0cd70e..d321c50 100644 --- a/src/P458/problem.jl +++ b/src/P458/problem.jl @@ -3,7 +3,7 @@ module Problem458 title = "Problem 458: Permutations of Project" published_on = "Sunday, 9th February 2014, 07:00 am" -solved_by = 939 +solved_by = 943 difficulty_rating = "30%" content = """ Consider the alphabet A made out of the letters of the word "project": A={c,e,j,o,p,r,t}. diff --git a/src/P46/problem.jl b/src/P46/problem.jl index 06b278b..31fd3ab 100644 --- a/src/P46/problem.jl +++ b/src/P46/problem.jl @@ -3,7 +3,7 @@ module Problem46 title = "Problem 46: Goldbach's other conjecture" published_on = "Friday, 20th June 2003, 06:00 pm" -solved_by = 64132 +solved_by = 64223 difficulty_rating = "5%" content = """ It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a diff --git a/src/P460/problem.jl b/src/P460/problem.jl index 5a22450..6d978d0 100644 --- a/src/P460/problem.jl +++ b/src/P460/problem.jl @@ -3,7 +3,7 @@ module Problem460 title = "Problem 460: An ant on the move" published_on = "Saturday, 22nd February 2014, 01:00 pm" -solved_by = 325 +solved_by = 327 difficulty_rating = "60%" content = """ diff --git a/src/P461/problem.jl b/src/P461/problem.jl index e44dc30..8ca3319 100644 --- a/src/P461/problem.jl +++ b/src/P461/problem.jl @@ -3,7 +3,7 @@ module Problem461 title = "Problem 461: Almost Pi" published_on = "Saturday, 1st March 2014, 04:00 pm" -solved_by = 1228 +solved_by = 1233 difficulty_rating = "30%" content = """ Let diff --git a/src/P462/problem.jl b/src/P462/problem.jl index 419e2af..534a8a6 100644 --- a/src/P462/problem.jl +++ b/src/P462/problem.jl @@ -3,7 +3,7 @@ module Problem462 title = "Problem 462: Permutation of 3-smooth numbers" published_on = "Saturday, 8th March 2014, 07:00 pm" -solved_by = 319 +solved_by = 322 difficulty_rating = "60%" content = """ A \e[1m3-smooth number\e[0m is an integer which has no prime factor larger than 3. For an integer N, we define S(N) as the set of 3- diff --git a/src/P463/problem.jl b/src/P463/problem.jl index e728c30..dabc04f 100644 --- a/src/P463/problem.jl +++ b/src/P463/problem.jl @@ -3,7 +3,7 @@ module Problem463 title = "Problem 463: A weird recurrence relation" published_on = "Saturday, 15th March 2014, 10:00 pm" -solved_by = 1108 +solved_by = 1115 difficulty_rating = "35%" content = """ The function f is defined for all positive integers as follows: diff --git a/src/P464/problem.jl b/src/P464/problem.jl index df61d18..7b068b6 100644 --- a/src/P464/problem.jl +++ b/src/P464/problem.jl @@ -3,7 +3,7 @@ module Problem464 title = "Problem 464: Möbius function and intervals" published_on = "Sunday, 23rd March 2014, 01:00 am" -solved_by = 325 +solved_by = 326 difficulty_rating = "60%" content = """ The \e[1mMöbius function,\e[0m denoted μ(n), is defined as: diff --git a/src/P465/problem.jl b/src/P465/problem.jl index 8395895..889c705 100644 --- a/src/P465/problem.jl +++ b/src/P465/problem.jl @@ -3,7 +3,7 @@ module Problem465 title = "Problem 465: Polar polygons" published_on = "Sunday, 30th March 2014, 05:00 am" -solved_by = 218 +solved_by = 220 difficulty_rating = "85%" content = """ The diff --git a/src/P466/problem.jl b/src/P466/problem.jl index 51cbd68..cc501e6 100644 --- a/src/P466/problem.jl +++ b/src/P466/problem.jl @@ -3,7 +3,7 @@ module Problem466 title = "Problem 466: Distinct terms in a multiplication table" published_on = "Sunday, 6th April 2014, 07:00 am" -solved_by = 315 +solved_by = 316 difficulty_rating = "65%" content = """ Let P(m,n) be the number of distinct terms in an m×n multiplication table. diff --git a/src/P467/problem.jl b/src/P467/problem.jl index a39185c..76a5c79 100644 --- a/src/P467/problem.jl +++ b/src/P467/problem.jl @@ -3,7 +3,7 @@ module Problem467 title = "Problem 467: Superinteger" published_on = "Sunday, 13th April 2014, 10:00 am" -solved_by = 442 +solved_by = 444 difficulty_rating = "50%" content = """ An integer s is called a superinteger of another integer n if the digits of n form a subsequence of the digits of s. diff --git a/src/P469/problem.jl b/src/P469/problem.jl index 727441a..12b3bfb 100644 --- a/src/P469/problem.jl +++ b/src/P469/problem.jl @@ -3,7 +3,7 @@ module Problem469 title = "Problem 469: Empty chairs" published_on = "Saturday, 26th April 2014, 04:00 pm" -solved_by = 758 +solved_by = 761 difficulty_rating = "40%" content = """ In a room N chairs are placed around a round table. diff --git a/src/P47/problem.jl b/src/P47/problem.jl index 6a0520b..8c8248a 100644 --- a/src/P47/problem.jl +++ b/src/P47/problem.jl @@ -3,7 +3,7 @@ module Problem47 title = "Problem 47: Distinct primes factors" published_on = "Friday, 4th July 2003, 06:00 pm" -solved_by = 60403 +solved_by = 60495 difficulty_rating = "5%" content = """ The first two consecutive numbers to have two distinct prime factors are: diff --git a/src/P473/problem.jl b/src/P473/problem.jl index 567584c..9ecc4eb 100644 --- a/src/P473/problem.jl +++ b/src/P473/problem.jl @@ -3,7 +3,7 @@ module Problem473 title = "Problem 473: Phigital number base" published_on = "Sunday, 25th May 2014, 04:00 am" -solved_by = 743 +solved_by = 746 difficulty_rating = "35%" content = """ diff --git a/src/P474/problem.jl b/src/P474/problem.jl index 19480b6..650ea70 100644 --- a/src/P474/problem.jl +++ b/src/P474/problem.jl @@ -3,7 +3,7 @@ module Problem474 title = "Problem 474: Last digits of divisors" published_on = "Sunday, 1st June 2014, 07:00 am" -solved_by = 421 +solved_by = 423 difficulty_rating = "50%" content = """ For a positive integer n and digits d, we define F(n, d) as the number of the divisors of n whose last digits equal d. diff --git a/src/P475/problem.jl b/src/P475/problem.jl index c614a06..616ec37 100644 --- a/src/P475/problem.jl +++ b/src/P475/problem.jl @@ -3,7 +3,7 @@ module Problem475 title = "Problem 475: Music festival" published_on = "Sunday, 8th June 2014, 10:00 am" -solved_by = 450 +solved_by = 454 difficulty_rating = "50%" content = """ 12n musicians participate at a music festival. On the first day, they form 3n quartets and practice all day. diff --git a/src/P476/problem.jl b/src/P476/problem.jl index 439a1ce..8047d0f 100644 --- a/src/P476/problem.jl +++ b/src/P476/problem.jl @@ -3,7 +3,7 @@ module Problem476 title = "Problem 476: Circle Packing II" published_on = "Saturday, 14th June 2014, 01:00 pm" -solved_by = 424 +solved_by = 425 difficulty_rating = "45%" content = """ Let R(a, b, c) be the maximum area covered by three non-overlapping circles inside a triangle with edge lengths a, b and c. diff --git a/src/P477/problem.jl b/src/P477/problem.jl index eec5873..7f3353c 100644 --- a/src/P477/problem.jl +++ b/src/P477/problem.jl @@ -3,7 +3,7 @@ module Problem477 title = "Problem 477: Number Sequence Game" published_on = "Saturday, 23rd August 2014, 04:00 pm" -solved_by = 264 +solved_by = 266 difficulty_rating = "65%" content = """ The number sequence game starts with a sequence S of N numbers written on a line. diff --git a/src/P479/problem.jl b/src/P479/problem.jl index 39bee71..834a8a1 100644 --- a/src/P479/problem.jl +++ b/src/P479/problem.jl @@ -3,7 +3,7 @@ module Problem479 title = "Problem 479: Roots on the Rise" published_on = "Saturday, 6th September 2014, 10:00 pm" -solved_by = 1309 +solved_by = 1315 difficulty_rating = "25%" content = """ Let a_k, b_k, and c_k represent the three solutions (real or complex numbers) to the equation diff --git a/src/P48/problem.jl b/src/P48/problem.jl index a3ad6a5..1fa004e 100644 --- a/src/P48/problem.jl +++ b/src/P48/problem.jl @@ -3,7 +3,7 @@ module Problem48 title = "Problem 48: Self powers" published_on = "Friday, 18th July 2003, 06:00 pm" -solved_by = 115552 +solved_by = 115690 difficulty_rating = "5%" content = """ The series, 1¹ + 2² + 3³ + ... + 10¹⁰ = 10405071317. diff --git a/src/P480/problem.jl b/src/P480/problem.jl index 6004e03..f0984d0 100644 --- a/src/P480/problem.jl +++ b/src/P480/problem.jl @@ -3,7 +3,7 @@ module Problem480 title = "Problem 480: The Last Question" published_on = "Sunday, 14th September 2014, 01:00 am" -solved_by = 584 +solved_by = 586 difficulty_rating = "45%" content = """ Consider all the words which can be formed by selecting letters, in any order, from the phrase: diff --git a/src/P482/problem.jl b/src/P482/problem.jl index 5109c7c..ab0163d 100644 --- a/src/P482/problem.jl +++ b/src/P482/problem.jl @@ -3,7 +3,7 @@ module Problem482 title = "Problem 482: The incenter of a triangle" published_on = "Sunday, 28th September 2014, 07:00 am" -solved_by = 217 +solved_by = 218 difficulty_rating = "85%" content = """ ABC is an integer sided triangle with incenter I and perimeter p. diff --git a/src/P483/problem.jl b/src/P483/problem.jl index 23f657c..66a1780 100644 --- a/src/P483/problem.jl +++ b/src/P483/problem.jl @@ -3,7 +3,7 @@ module Problem483 title = "Problem 483: Repeated permutation" published_on = "Sunday, 5th October 2014, 10:00 am" -solved_by = 228 +solved_by = 229 difficulty_rating = "100%" content = """ We define a permutation as an operation that rearranges the order of the elements {1, 2, 3, ..., n}. There are n! such diff --git a/src/P484/problem.jl b/src/P484/problem.jl index bbb4f85..bcad744 100644 --- a/src/P484/problem.jl +++ b/src/P484/problem.jl @@ -3,7 +3,7 @@ module Problem484 title = "Problem 484: Arithmetic Derivative" published_on = "Saturday, 11th October 2014, 01:00 pm" -solved_by = 367 +solved_by = 369 difficulty_rating = "100%" content = """ The \e[1marithmetic derivative\e[0m is defined by diff --git a/src/P485/problem.jl b/src/P485/problem.jl index 8e49afb..daba4c5 100644 --- a/src/P485/problem.jl +++ b/src/P485/problem.jl @@ -3,7 +3,7 @@ module Problem485 title = "Problem 485: Maximum number of divisors" published_on = "Saturday, 18th October 2014, 04:00 pm" -solved_by = 1174 +solved_by = 1181 difficulty_rating = "30%" content = """ Let d(n) be the number of divisors of n. diff --git a/src/P487/problem.jl b/src/P487/problem.jl index b3d51b5..0c65fa9 100644 --- a/src/P487/problem.jl +++ b/src/P487/problem.jl @@ -3,7 +3,7 @@ module Problem487 title = "Problem 487: Sums of power sums" published_on = "Saturday, 1st November 2014, 10:00 pm" -solved_by = 655 +solved_by = 658 difficulty_rating = "40%" content = """ Let fₖ(n) be the sum of the kᵗʰ powers of the first n positive integers. diff --git a/src/P489/problem.jl b/src/P489/problem.jl index e33bc08..59fb5b7 100644 --- a/src/P489/problem.jl +++ b/src/P489/problem.jl @@ -3,7 +3,7 @@ module Problem489 title = "Problem 489: Common factors between two sequences" published_on = "Sunday, 16th November 2014, 04:00 am" -solved_by = 244 +solved_by = 245 difficulty_rating = "100%" content = """ Let G(a, b) be the smallest non-negative integer n for which gcd(n³ + b, (n + a)³ + b) is maximized. diff --git a/src/P49/problem.jl b/src/P49/problem.jl index e202557..12ff464 100644 --- a/src/P49/problem.jl +++ b/src/P49/problem.jl @@ -3,7 +3,7 @@ module Problem49 title = "Problem 49: Prime permutations" published_on = "Friday, 1st August 2003, 06:00 pm" -solved_by = 60299 +solved_by = 60390 difficulty_rating = "5%" content = """ The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of diff --git a/src/P491/problem.jl b/src/P491/problem.jl index 4ebf8d9..03399d8 100644 --- a/src/P491/problem.jl +++ b/src/P491/problem.jl @@ -3,7 +3,7 @@ module Problem491 title = "Problem 491: Double pandigital number divisible by 11" published_on = "Sunday, 30th November 2014, 10:00 am" -solved_by = 2193 +solved_by = 2200 difficulty_rating = "20%" content = """ We call a positive integer double pandigital if it uses all the digits 0 to 9 exactly twice (with no leading zero). For example, diff --git a/src/P492/problem.jl b/src/P492/problem.jl index 5859702..eca41c2 100644 --- a/src/P492/problem.jl +++ b/src/P492/problem.jl @@ -3,7 +3,7 @@ module Problem492 title = "Problem 492: Exploding sequence" published_on = "Saturday, 6th December 2014, 01:00 pm" -solved_by = 358 +solved_by = 361 difficulty_rating = "60%" content = """ Define the sequence a₁, a₂, a₃, ... as: diff --git a/src/P493/problem.jl b/src/P493/problem.jl index 5088bbd..9c0a86a 100644 --- a/src/P493/problem.jl +++ b/src/P493/problem.jl @@ -3,7 +3,7 @@ module Problem493 title = "Problem 493: Under The Rainbow" published_on = "Saturday, 13th December 2014, 04:00 pm" -solved_by = 5433 +solved_by = 5447 difficulty_rating = "10%" content = """ 70 coloured balls are placed in an urn, 10 for each of the seven rainbow colours. diff --git a/src/P495/problem.jl b/src/P495/problem.jl index d45b984..c9f788c 100644 --- a/src/P495/problem.jl +++ b/src/P495/problem.jl @@ -3,7 +3,7 @@ module Problem495 title = "Problem 495: Writing n as the product of k distinct positive integers" published_on = "Saturday, 27th December 2014, 10:00 pm" -solved_by = 293 +solved_by = 295 difficulty_rating = "100%" content = """ Let W(n,k) be the number of ways in which n can be written as the product of k distinct positive integers. diff --git a/src/P496/problem.jl b/src/P496/problem.jl index 755f505..b5b4a13 100644 --- a/src/P496/problem.jl +++ b/src/P496/problem.jl @@ -3,7 +3,7 @@ module Problem496 title = "Problem 496: Incenter and circumcenter of triangle" published_on = "Sunday, 4th January 2015, 01:00 am" -solved_by = 307 +solved_by = 309 difficulty_rating = "50%" content = """ Given an integer sided triangle ABC: diff --git a/src/P497/problem.jl b/src/P497/problem.jl index ab54c5f..ac35f6c 100644 --- a/src/P497/problem.jl +++ b/src/P497/problem.jl @@ -3,7 +3,7 @@ module Problem497 title = "Problem 497: Drunken Tower of Hanoi" published_on = "Sunday, 11th January 2015, 04:00 am" -solved_by = 550 +solved_by = 553 difficulty_rating = "40%" content = """ Bob is very familiar with the famous mathematical puzzle/game, "Tower of Hanoi," which consists of three upright rods and disks of different sizes that can slide onto any of the rods. The game begins with a stack of diff --git a/src/P498/problem.jl b/src/P498/problem.jl index 58e48eb..bafb2b6 100644 --- a/src/P498/problem.jl +++ b/src/P498/problem.jl @@ -3,7 +3,7 @@ module Problem498 title = "Problem 498: Remainder of polynomial division" published_on = "Sunday, 18th January 2015, 07:00 am" -solved_by = 523 +solved_by = 526 difficulty_rating = "40%" content = """ For positive integers n and m, we define two polynomials Fₙ(x) = xⁿ and Gₘ(x) = (x-1)ᵐ. diff --git a/src/P499/problem.jl b/src/P499/problem.jl index 63499d5..ce5e16d 100644 --- a/src/P499/problem.jl +++ b/src/P499/problem.jl @@ -3,7 +3,7 @@ module Problem499 title = "Problem 499: St. Petersburg Lottery" published_on = "Sunday, 25th January 2015, 10:00 am" -solved_by = 335 +solved_by = 336 difficulty_rating = "100%" content = """ A gambler decides to participate in a special lottery. In this lottery the gambler plays a series of one or more games. diff --git a/src/P5/problem.jl b/src/P5/problem.jl index d822f96..7d8d457 100644 --- a/src/P5/problem.jl +++ b/src/P5/problem.jl @@ -3,7 +3,7 @@ module Problem5 title = "Problem 5: Smallest multiple" published_on = "Friday, 30th November 2001, 06:00 pm" -solved_by = 497304 +solved_by = 497519 difficulty_rating = "5%" content = """ 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. diff --git a/src/P50/problem.jl b/src/P50/problem.jl index e131ccb..b3c4e4a 100644 --- a/src/P50/problem.jl +++ b/src/P50/problem.jl @@ -3,7 +3,7 @@ module Problem50 title = "Problem 50: Consecutive prime sum" published_on = "Friday, 15th August 2003, 06:00 pm" -solved_by = 64956 +solved_by = 65067 difficulty_rating = "5%" content = """ The prime 41, can be written as the sum of six consecutive primes: diff --git a/src/P500/problem.jl b/src/P500/problem.jl index 8c0f3d3..6e30bd3 100644 --- a/src/P500/problem.jl +++ b/src/P500/problem.jl @@ -3,7 +3,7 @@ module Problem500 title = "Problem 500: Problem 500!!!" published_on = "Saturday, 31st January 2015, 01:00 pm" -solved_by = 4088 +solved_by = 4110 difficulty_rating = "15%" content = """ The number of divisors of 120 is 16. diff --git a/src/P501/problem.jl b/src/P501/problem.jl index 38b46e2..d0f0d0b 100644 --- a/src/P501/problem.jl +++ b/src/P501/problem.jl @@ -3,7 +3,7 @@ module Problem501 title = "Problem 501: Eight Divisors" published_on = "Saturday, 31st January 2015, 01:00 pm" -solved_by = 1366 +solved_by = 1377 difficulty_rating = "40%" content = """ The eight divisors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The ten numbers not exceeding 100 having exactly eight divisors are 24, diff --git a/src/P502/problem.jl b/src/P502/problem.jl index 9cd195f..af1d6eb 100644 --- a/src/P502/problem.jl +++ b/src/P502/problem.jl @@ -3,7 +3,7 @@ module Problem502 title = "Problem 502: Counting Castles" published_on = "Saturday, 7th February 2015, 04:00 pm" -solved_by = 292 +solved_by = 295 difficulty_rating = "100%" content = """ We define a diff --git a/src/P503/problem.jl b/src/P503/problem.jl index a1a2357..176cfda 100644 --- a/src/P503/problem.jl +++ b/src/P503/problem.jl @@ -3,7 +3,7 @@ module Problem503 title = "Problem 503: Compromise or persist" published_on = "Saturday, 14th February 2015, 07:00 pm" -solved_by = 319 +solved_by = 324 difficulty_rating = "60%" content = """ Alice is playing a game with n cards numbered 1 to n. diff --git a/src/P504/problem.jl b/src/P504/problem.jl index 2643b52..c91e8d9 100644 --- a/src/P504/problem.jl +++ b/src/P504/problem.jl @@ -3,7 +3,7 @@ module Problem504 title = "Problem 504: Square on the Inside" published_on = "Saturday, 21st February 2015, 10:00 pm" -solved_by = 3113 +solved_by = 3124 difficulty_rating = "15%" content = """ Let ABCD be a quadrilateral whose vertices are lattice points lying on the coordinate axes as follows: diff --git a/src/P505/problem.jl b/src/P505/problem.jl index 7c0084c..39adff5 100644 --- a/src/P505/problem.jl +++ b/src/P505/problem.jl @@ -3,7 +3,7 @@ module Problem505 title = "Problem 505: Bidirectional Recurrence" published_on = "Sunday, 1st March 2015, 01:00 am" -solved_by = 208 +solved_by = 209 difficulty_rating = "90%" content = """ Let: diff --git a/src/P506/problem.jl b/src/P506/problem.jl index 3d84cb4..c585323 100644 --- a/src/P506/problem.jl +++ b/src/P506/problem.jl @@ -3,7 +3,7 @@ module Problem506 title = "Problem 506: Clock sequence" published_on = "Sunday, 8th March 2015, 04:00 am" -solved_by = 881 +solved_by = 887 difficulty_rating = "30%" content = """ Consider the infinite repeating sequence of digits: diff --git a/src/P507/problem.jl b/src/P507/problem.jl index 1623af9..ca17da4 100644 --- a/src/P507/problem.jl +++ b/src/P507/problem.jl @@ -3,7 +3,7 @@ module Problem507 title = "Problem 507: Shortest Lattice Vector" published_on = "Sunday, 15th March 2015, 07:00 am" -solved_by = 217 +solved_by = 218 difficulty_rating = "90%" content = """ Let tₙ be the tribonacci numbers defined as: diff --git a/src/P509/problem.jl b/src/P509/problem.jl index 7391700..e13eecc 100644 --- a/src/P509/problem.jl +++ b/src/P509/problem.jl @@ -3,7 +3,7 @@ module Problem509 title = "Problem 509: Divisor Nim" published_on = "Saturday, 28th March 2015, 01:00 pm" -solved_by = 572 +solved_by = 577 difficulty_rating = "45%" content = """ Anton and Bertrand love to play three pile Nim. diff --git a/src/P51/problem.jl b/src/P51/problem.jl index e09df27..51ddbd2 100644 --- a/src/P51/problem.jl +++ b/src/P51/problem.jl @@ -3,7 +3,7 @@ module Problem51 title = "Problem 51: Prime digit replacements" published_on = "Friday, 29th August 2003, 06:00 pm" -solved_by = 35591 +solved_by = 35677 difficulty_rating = "15%" content = """ By replacing the 1ˢᵗ digit of the 2-digit number *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are diff --git a/src/P510/problem.jl b/src/P510/problem.jl index 140a2d4..1a50c90 100644 --- a/src/P510/problem.jl +++ b/src/P510/problem.jl @@ -3,7 +3,7 @@ module Problem510 title = "Problem 510: Tangent Circles" published_on = "Saturday, 4th April 2015, 04:00 pm" -solved_by = 1038 +solved_by = 1039 difficulty_rating = "30%" content = """ Circles A and B are tangent to each other and to line L at three distinct points. diff --git a/src/P511/problem.jl b/src/P511/problem.jl index d472b82..a2367e1 100644 --- a/src/P511/problem.jl +++ b/src/P511/problem.jl @@ -3,7 +3,7 @@ module Problem511 title = "Problem 511: Sequences with nice divisibility properties" published_on = "Saturday, 11th April 2015, 07:00 pm" -solved_by = 411 +solved_by = 417 difficulty_rating = "55%" content = """ Let Seq(n,k) be the number of positive-integer sequences {aᵢ}₁≤ᵢ≤ₙ of length n such that: diff --git a/src/P512/problem.jl b/src/P512/problem.jl index 6b8cace..45ba56b 100644 --- a/src/P512/problem.jl +++ b/src/P512/problem.jl @@ -3,7 +3,7 @@ module Problem512 title = "Problem 512: Sums of totients of powers" published_on = "Saturday, 18th April 2015, 10:00 pm" -solved_by = 1524 +solved_by = 1530 difficulty_rating = "25%" content = """ Let φ(n) be Euler's totient function. diff --git a/src/P513/problem.jl b/src/P513/problem.jl index 0defa76..2eb32e4 100644 --- a/src/P513/problem.jl +++ b/src/P513/problem.jl @@ -3,7 +3,7 @@ module Problem513 title = "Problem 513: Integral median" published_on = "Sunday, 26th April 2015, 01:00 am" -solved_by = 309 +solved_by = 310 difficulty_rating = "60%" content = """ ABC is an integral sided triangle with sides a≤b≤c. diff --git a/src/P514/problem.jl b/src/P514/problem.jl index b0a8e4d..066dfa7 100644 --- a/src/P514/problem.jl +++ b/src/P514/problem.jl @@ -3,7 +3,7 @@ module Problem514 title = "Problem 514: Geoboard Shapes" published_on = "Sunday, 3rd May 2015, 04:00 am" -solved_by = 212 +solved_by = 214 difficulty_rating = "90%" content = """ A diff --git a/src/P515/problem.jl b/src/P515/problem.jl index 241901d..4e4ee45 100644 --- a/src/P515/problem.jl +++ b/src/P515/problem.jl @@ -3,7 +3,7 @@ module Problem515 title = "Problem 515: Dissonant Numbers" published_on = "Sunday, 10th May 2015, 07:00 am" -solved_by = 467 +solved_by = 470 difficulty_rating = "40%" content = """ Let d(p,n,0) be the multiplicative inverse of n modulo prime p, defined as n × d(p,n,0) = 1 mod p. diff --git a/src/P516/problem.jl b/src/P516/problem.jl index 556a021..5e5e940 100644 --- a/src/P516/problem.jl +++ b/src/P516/problem.jl @@ -3,7 +3,7 @@ module Problem516 title = "Problem 516: 5-smooth totients" published_on = "Sunday, 17th May 2015, 10:00 am" -solved_by = 1588 +solved_by = 1592 difficulty_rating = "20%" content = """ 5-smooth numbers are numbers whose largest prime factor doesn't exceed 5. diff --git a/src/P517/problem.jl b/src/P517/problem.jl index 60b9b4d..90729bb 100644 --- a/src/P517/problem.jl +++ b/src/P517/problem.jl @@ -3,7 +3,7 @@ module Problem517 title = "Problem 517: A real recursion" published_on = "Saturday, 23rd May 2015, 01:00 pm" -solved_by = 463 +solved_by = 466 difficulty_rating = "45%" content = """ diff --git a/src/P518/problem.jl b/src/P518/problem.jl index d51f75c..5030b16 100644 --- a/src/P518/problem.jl +++ b/src/P518/problem.jl @@ -3,7 +3,7 @@ module Problem518 title = "Problem 518: Prime triples and geometric sequences" published_on = "Saturday, 30th May 2015, 04:00 pm" -solved_by = 1625 +solved_by = 1637 difficulty_rating = "20%" content = """ Let S(n) = Σ a+b+c over all triples (a,b,c) such that: diff --git a/src/P519/problem.jl b/src/P519/problem.jl index 405461f..2696119 100644 --- a/src/P519/problem.jl +++ b/src/P519/problem.jl @@ -3,7 +3,7 @@ module Problem519 title = "Problem 519: Tricoloured Coin Fountains" published_on = "Saturday, 6th June 2015, 07:00 pm" -solved_by = 343 +solved_by = 345 difficulty_rating = "50%" content = """ An arrangement of coins in one or more rows with the bottom row being a block without gaps and every coin in a higher row touching exactly two coins in the row below is called a diff --git a/src/P52/problem.jl b/src/P52/problem.jl index 4fefcb1..f6e79d9 100644 --- a/src/P52/problem.jl +++ b/src/P52/problem.jl @@ -3,7 +3,7 @@ module Problem52 title = "Problem 52: Permuted multiples" published_on = "Friday, 12th September 2003, 06:00 pm" -solved_by = 67611 +solved_by = 67710 difficulty_rating = "5%" content = """ It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order. diff --git a/src/P520/problem.jl b/src/P520/problem.jl index 0273881..21158e8 100644 --- a/src/P520/problem.jl +++ b/src/P520/problem.jl @@ -3,7 +3,7 @@ module Problem520 title = "Problem 520: Simbers" published_on = "Saturday, 13th June 2015, 10:00 pm" -solved_by = 409 +solved_by = 410 difficulty_rating = "45%" content = """ We define a simber to be a positive integer in which any odd digit, if present, occurs an odd number of times, and any even diff --git a/src/P521/problem.jl b/src/P521/problem.jl index 79f1525..5ed0936 100644 --- a/src/P521/problem.jl +++ b/src/P521/problem.jl @@ -3,7 +3,7 @@ module Problem521 title = "Problem 521: Smallest prime factor" published_on = "Sunday, 21st June 2015, 01:00 am" -solved_by = 742 +solved_by = 749 difficulty_rating = "50%" content = """ Let smpf(n) be the smallest prime factor of n. diff --git a/src/P523/problem.jl b/src/P523/problem.jl index 51fa750..60ee512 100644 --- a/src/P523/problem.jl +++ b/src/P523/problem.jl @@ -3,7 +3,7 @@ module Problem523 title = "Problem 523: First Sort I" published_on = "Sunday, 6th September 2015, 07:00 am" -solved_by = 1000 +solved_by = 1003 difficulty_rating = "30%" content = """ Consider the following algorithm for sorting a list: diff --git a/src/P525/problem.jl b/src/P525/problem.jl index d066f9b..52dc05c 100644 --- a/src/P525/problem.jl +++ b/src/P525/problem.jl @@ -3,7 +3,7 @@ module Problem525 title = "Problem 525: Rolling Ellipse" published_on = "Sunday, 13th September 2015, 10:00 am" -solved_by = 507 +solved_by = 513 difficulty_rating = "45%" content = """ An ellipse diff --git a/src/P527/problem.jl b/src/P527/problem.jl index 23ca4d4..47c6895 100644 --- a/src/P527/problem.jl +++ b/src/P527/problem.jl @@ -3,7 +3,7 @@ module Problem527 title = "Problem 527: Randomized Binary Search" published_on = "Saturday, 26th September 2015, 04:00 pm" -solved_by = 743 +solved_by = 747 difficulty_rating = "30%" content = """ A secret integer t is selected at random within the range 1 ≤ t ≤ n. diff --git a/src/P528/problem.jl b/src/P528/problem.jl index 0eda084..4cb9b11 100644 --- a/src/P528/problem.jl +++ b/src/P528/problem.jl @@ -3,7 +3,7 @@ module Problem528 title = "Problem 528: Constrained Sums" published_on = "Saturday, 3rd October 2015, 07:00 pm" -solved_by = 275 +solved_by = 276 difficulty_rating = "60%" content = """ Let S(n,k,b) represent the number of valid solutions to x₁ + x₂ + ... + xₖ ≤ n, where 0 ≤ xₘ ≤ bᵐ for all 1 ≤ m ≤ k. diff --git a/src/P53/problem.jl b/src/P53/problem.jl index 6a5751a..96a9c19 100644 --- a/src/P53/problem.jl +++ b/src/P53/problem.jl @@ -3,7 +3,7 @@ module Problem53 title = "Problem 53: Combinatoric selections" published_on = "Friday, 26th September 2003, 06:00 pm" -solved_by = 61140 +solved_by = 61237 difficulty_rating = "5%" content = """ There are exactly ten ways of selecting three from five, 12345: diff --git a/src/P530/problem.jl b/src/P530/problem.jl index 4c54a41..19ac8e3 100644 --- a/src/P530/problem.jl +++ b/src/P530/problem.jl @@ -3,7 +3,7 @@ module Problem530 title = "Problem 530: GCD of Divisors" published_on = "Sunday, 18th October 2015, 01:00 am" -solved_by = 451 +solved_by = 452 difficulty_rating = "60%" content = """ Every divisor diff --git a/src/P531/problem.jl b/src/P531/problem.jl index 9b7244f..e9fe10e 100644 --- a/src/P531/problem.jl +++ b/src/P531/problem.jl @@ -3,7 +3,7 @@ module Problem531 title = "Problem 531: Chinese leftovers" published_on = "Sunday, 25th October 2015, 04:00 am" -solved_by = 1158 +solved_by = 1162 difficulty_rating = "25%" content = """ Let g(a,n,b,m) be the smallest non-negative solution x to the system: diff --git a/src/P532/problem.jl b/src/P532/problem.jl index 2c4b19e..6f38ee3 100644 --- a/src/P532/problem.jl +++ b/src/P532/problem.jl @@ -3,7 +3,7 @@ module Problem532 title = "Problem 532: Nanobots on Geodesics" published_on = "Sunday, 1st November 2015, 07:00 am" -solved_by = 310 +solved_by = 312 difficulty_rating = "55%" content = """ Bob is a manufacturer of nanobots and wants to impress his customers by giving them a ball coloured by his new nanobots as a present. diff --git a/src/P533/problem.jl b/src/P533/problem.jl index 5c509d8..7843aae 100644 --- a/src/P533/problem.jl +++ b/src/P533/problem.jl @@ -3,7 +3,7 @@ module Problem533 title = "Problem 533: Minimum values of the Carmichael function" published_on = "Sunday, 8th November 2015, 10:00 am" -solved_by = 329 +solved_by = 334 difficulty_rating = "50%" content = """ The \e[1mCarmichael function\e[0m λ(n) is defined as the smallest positive integer m such that aᵐ = 1 modulo n for all integers a diff --git a/src/P534/problem.jl b/src/P534/problem.jl index 72b4d76..ccc3fb9 100644 --- a/src/P534/problem.jl +++ b/src/P534/problem.jl @@ -3,7 +3,7 @@ module Problem534 title = "Problem 534: Weak Queens" published_on = "Saturday, 14th November 2015, 01:00 pm" -solved_by = 307 +solved_by = 311 difficulty_rating = "55%" content = """ The classical diff --git a/src/P535/problem.jl b/src/P535/problem.jl index ffbbf2e..8eb0c70 100644 --- a/src/P535/problem.jl +++ b/src/P535/problem.jl @@ -3,7 +3,7 @@ module Problem535 title = "Problem 535: Fractal Sequence" published_on = "Saturday, 21st November 2015, 04:00 pm" -solved_by = 289 +solved_by = 291 difficulty_rating = "60%" content = """ Consider the infinite integer sequence S starting with: diff --git a/src/P536/problem.jl b/src/P536/problem.jl index 9da3e1e..eab1b72 100644 --- a/src/P536/problem.jl +++ b/src/P536/problem.jl @@ -3,7 +3,7 @@ module Problem536 title = "Problem 536: Modulo power identity" published_on = "Saturday, 28th November 2015, 07:00 pm" -solved_by = 288 +solved_by = 289 difficulty_rating = "60%" content = """ Let S(n) be the sum of all positive integers m not exceeding n having the following property: diff --git a/src/P537/problem.jl b/src/P537/problem.jl index 24cbee2..8f5f994 100644 --- a/src/P537/problem.jl +++ b/src/P537/problem.jl @@ -3,7 +3,7 @@ module Problem537 title = "Problem 537: Counting tuples" published_on = "Saturday, 5th December 2015, 10:00 pm" -solved_by = 623 +solved_by = 627 difficulty_rating = "35%" content = """ diff --git a/src/P538/problem.jl b/src/P538/problem.jl index 6b8e178..d33b884 100644 --- a/src/P538/problem.jl +++ b/src/P538/problem.jl @@ -3,7 +3,7 @@ module Problem538 title = "Problem 538: Maximum quadrilaterals" published_on = "Sunday, 13th December 2015, 01:00 am" -solved_by = 327 +solved_by = 329 difficulty_rating = "40%" content = """ Consider a positive integer sequence S = (s₁, s₂, ..., sₙ). diff --git a/src/P539/problem.jl b/src/P539/problem.jl index dcaa8e7..c5ca513 100644 --- a/src/P539/problem.jl +++ b/src/P539/problem.jl @@ -3,7 +3,7 @@ module Problem539 title = "Problem 539: Odd elimination" published_on = "Sunday, 20th December 2015, 04:00 am" -solved_by = 824 +solved_by = 826 difficulty_rating = "35%" content = """ diff --git a/src/P54/problem.jl b/src/P54/problem.jl index 9daa04f..a87f859 100644 --- a/src/P54/problem.jl +++ b/src/P54/problem.jl @@ -3,7 +3,7 @@ module Problem54 title = "Problem 54: Poker hands" published_on = "Friday, 10th October 2003, 06:00 pm" -solved_by = 37739 +solved_by = 37817 difficulty_rating = "10%" content = """ In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way: diff --git a/src/P540/problem.jl b/src/P540/problem.jl index 5d031f1..b099d39 100644 --- a/src/P540/problem.jl +++ b/src/P540/problem.jl @@ -3,7 +3,7 @@ module Problem540 title = "Problem 540: Counting primitive Pythagorean triples" published_on = "Sunday, 27th December 2015, 07:00 am" -solved_by = 651 +solved_by = 655 difficulty_rating = "30%" content = """ A \e[1mPythagorean triple\e[0m consists of three positive integers a, b and c satisfying a²+b²=c². diff --git a/src/P543/problem.jl b/src/P543/problem.jl index 08f7030..39d8b6b 100644 --- a/src/P543/problem.jl +++ b/src/P543/problem.jl @@ -3,7 +3,7 @@ module Problem543 title = "Problem 543: Prime-Sum Numbers" published_on = "Saturday, 16th January 2016, 04:00 pm" -solved_by = 692 +solved_by = 698 difficulty_rating = "30%" content = """ Define function P(n,k) = 1 if n can be written as the sum of k prime numbers (with repetitions allowed), and P(n,k) = 0 diff --git a/src/P544/problem.jl b/src/P544/problem.jl index 04423f2..4499444 100644 --- a/src/P544/problem.jl +++ b/src/P544/problem.jl @@ -3,7 +3,7 @@ module Problem544 title = "Problem 544: Chromatic Conundrum" published_on = "Saturday, 23rd January 2016, 07:00 pm" -solved_by = 247 +solved_by = 252 difficulty_rating = "90%" content = """ Let F(r,c,n) be the number of ways to colour a rectangular grid with r rows and c columns using at most n colours such that no diff --git a/src/P545/problem.jl b/src/P545/problem.jl index d3320e5..c9ae3dc 100644 --- a/src/P545/problem.jl +++ b/src/P545/problem.jl @@ -3,7 +3,7 @@ module Problem545 title = "Problem 545: Faulhaber's Formulas" published_on = "Saturday, 30th January 2016, 10:00 pm" -solved_by = 531 +solved_by = 535 difficulty_rating = "35%" content = """ The sum of the diff --git a/src/P546/problem.jl b/src/P546/problem.jl index 4153e37..4ffd38e 100644 --- a/src/P546/problem.jl +++ b/src/P546/problem.jl @@ -3,7 +3,7 @@ module Problem546 title = "Problem 546: The Floor's Revenge" published_on = "Sunday, 7th February 2016, 01:00 am" -solved_by = 230 +solved_by = 232 difficulty_rating = "85%" content = """ Define diff --git a/src/P547/problem.jl b/src/P547/problem.jl index e2435e4..32e38f1 100644 --- a/src/P547/problem.jl +++ b/src/P547/problem.jl @@ -3,7 +3,7 @@ module Problem547 title = "Problem 547: Distance of random points within hollow square laminae" published_on = "Sunday, 14th February 2016, 04:00 am" -solved_by = 221 +solved_by = 223 difficulty_rating = "70%" content = """ Assuming that two points are chosen randomly (with \e[1muniform distribution\e[0m]) within a rectangle, it is possible to determine the diff --git a/src/P548/problem.jl b/src/P548/problem.jl index 69b12d5..8866d06 100644 --- a/src/P548/problem.jl +++ b/src/P548/problem.jl @@ -3,7 +3,7 @@ module Problem548 title = "Problem 548: Gozinta Chains" published_on = "Sunday, 21st February 2016, 07:00 am" -solved_by = 611 +solved_by = 615 difficulty_rating = "35%" content = """ A \e[1mgozinta chain\e[0m for n is a sequence {1,a,b,...,n} where each element properly divides the next. diff --git a/src/P549/problem.jl b/src/P549/problem.jl index 560bd7a..392f256 100644 --- a/src/P549/problem.jl +++ b/src/P549/problem.jl @@ -3,7 +3,7 @@ module Problem549 title = "Problem 549: Divisibility of factorials" published_on = "Sunday, 28th February 2016, 10:00 am" -solved_by = 2762 +solved_by = 2775 difficulty_rating = "15%" content = """ The smallest number m such that 10 divides m! is m=5. diff --git a/src/P55/problem.jl b/src/P55/problem.jl index c0fd2d9..a2d58a1 100644 --- a/src/P55/problem.jl +++ b/src/P55/problem.jl @@ -3,7 +3,7 @@ module Problem55 title = "Problem 55: Lychrel numbers" published_on = "Friday, 24th October 2003, 06:00 pm" -solved_by = 55881 +solved_by = 55977 difficulty_rating = "5%" content = """ If we take 47, reverse and add, 47 + 74 = 121, which is palindromic. diff --git a/src/P550/problem.jl b/src/P550/problem.jl index 6b3ab7b..9540316 100644 --- a/src/P550/problem.jl +++ b/src/P550/problem.jl @@ -3,7 +3,7 @@ module Problem550 title = "Problem 550: Divisor game" published_on = "Saturday, 5th March 2016, 01:00 pm" -solved_by = 347 +solved_by = 348 difficulty_rating = "60%" content = """ Two players are playing a game, alternating turns. There are k piles of stones. On each turn, a player has to choose a pile and diff --git a/src/P551/problem.jl b/src/P551/problem.jl index 2d8bc8f..7c7b5bc 100644 --- a/src/P551/problem.jl +++ b/src/P551/problem.jl @@ -3,7 +3,7 @@ module Problem551 title = "Problem 551: Sum of digits sequence" published_on = "Saturday, 12th March 2016, 04:00 pm" -solved_by = 466 +solved_by = 469 difficulty_rating = "50%" content = """ Let a₀, a₁, a₂, ... be an integer sequence defined by: diff --git a/src/P552/problem.jl b/src/P552/problem.jl index 02d9084..5c4add9 100644 --- a/src/P552/problem.jl +++ b/src/P552/problem.jl @@ -3,7 +3,7 @@ module Problem552 title = "Problem 552: Chinese leftovers II" published_on = "Saturday, 19th March 2016, 07:00 pm" -solved_by = 438 +solved_by = 440 difficulty_rating = "40%" content = """ Let Aₙ be the smallest positive integer satisfying Aₙ mod pᵢ = i for all 1 ≤ i ≤ n, where pᵢ is the i-th prime. diff --git a/src/P553/problem.jl b/src/P553/problem.jl index 598aef5..454fb7f 100644 --- a/src/P553/problem.jl +++ b/src/P553/problem.jl @@ -3,7 +3,7 @@ module Problem553 title = "Problem 553: Power sets of power sets" published_on = "Saturday, 26th March 2016, 10:00 pm" -solved_by = 208 +solved_by = 210 difficulty_rating = "85%" content = """ Let diff --git a/src/P554/problem.jl b/src/P554/problem.jl index 2e8047a..277e17e 100644 --- a/src/P554/problem.jl +++ b/src/P554/problem.jl @@ -3,7 +3,7 @@ module Problem554 title = "Problem 554: Centaurs on a chess board" published_on = "Sunday, 3rd April 2016, 01:00 am" -solved_by = 242 +solved_by = 243 difficulty_rating = "80%" content = """ On a chess board, a centaur moves like a king or a knight. The diagram below shows the valid moves of a centaur (represented by an inverted king) on an 8x8 board. diff --git a/src/P555/problem.jl b/src/P555/problem.jl index 26a96cf..0f1ebbd 100644 --- a/src/P555/problem.jl +++ b/src/P555/problem.jl @@ -3,7 +3,7 @@ module Problem555 title = "Problem 555: McCarthy 91 function" published_on = "Sunday, 10th April 2016, 04:00 am" -solved_by = 696 +solved_by = 700 difficulty_rating = "30%" content = """ diff --git a/src/P557/problem.jl b/src/P557/problem.jl index 1c28ba9..1cfd095 100644 --- a/src/P557/problem.jl +++ b/src/P557/problem.jl @@ -3,7 +3,7 @@ module Problem557 title = "Problem 557: Cutting triangles" published_on = "Sunday, 24th April 2016, 10:00 am" -solved_by = 288 +solved_by = 292 difficulty_rating = "55%" content = """ diff --git a/src/P56/problem.jl b/src/P56/problem.jl index 0ef1a0e..aaa841d 100644 --- a/src/P56/problem.jl +++ b/src/P56/problem.jl @@ -3,7 +3,7 @@ module Problem56 title = "Problem 56: Powerful digit sum" published_on = "Friday, 7th November 2003, 06:00 pm" -solved_by = 60337 +solved_by = 60444 difficulty_rating = "5%" content = """ A googol (10¹⁰⁰) is a massive number: one followed by one-hundred zeros; 100¹⁰⁰ is almost unimaginably large: one followed diff --git a/src/P560/problem.jl b/src/P560/problem.jl index a15de69..1fcb601 100644 --- a/src/P560/problem.jl +++ b/src/P560/problem.jl @@ -3,7 +3,7 @@ module Problem560 title = "Problem 560: Coprime Nim" published_on = "Saturday, 14th May 2016, 07:00 pm" -solved_by = 314 +solved_by = 317 difficulty_rating = "75%" content = """ Coprime Nim is just like ordinary normal play Nim, but the players may only remove a number of stones from a pile that is diff --git a/src/P561/problem.jl b/src/P561/problem.jl index 11d2293..786d0ee 100644 --- a/src/P561/problem.jl +++ b/src/P561/problem.jl @@ -3,7 +3,7 @@ module Problem561 title = "Problem 561: Divisor Pairs" published_on = "Saturday, 21st May 2016, 10:00 pm" -solved_by = 766 +solved_by = 777 difficulty_rating = "30%" content = """ Let S(n) be the number of pairs (a,b) of distinct divisors of n such that a divides b. diff --git a/src/P562/problem.jl b/src/P562/problem.jl index ed5f9dd..400b5c3 100644 --- a/src/P562/problem.jl +++ b/src/P562/problem.jl @@ -3,7 +3,7 @@ module Problem562 title = "Problem 562: Maximal perimeter" published_on = "Sunday, 29th May 2016, 01:00 am" -solved_by = 190 +solved_by = 191 difficulty_rating = "75%" content = """ Construct triangle ABC such that: diff --git a/src/P563/problem.jl b/src/P563/problem.jl index d698713..5bb052b 100644 --- a/src/P563/problem.jl +++ b/src/P563/problem.jl @@ -3,7 +3,7 @@ module Problem563 title = "Problem 563: Robot Welders" published_on = "Sunday, 5th June 2016, 04:00 am" -solved_by = 326 +solved_by = 330 difficulty_rating = "45%" content = """ A company specialises in producing large rectangular metal sheets, starting from unit square metal plates. The welding is diff --git a/src/P565/problem.jl b/src/P565/problem.jl index 51b1d4c..d4bc08c 100644 --- a/src/P565/problem.jl +++ b/src/P565/problem.jl @@ -3,7 +3,7 @@ module Problem565 title = "Problem 565: Divisibility of sum of divisors" published_on = "Sunday, 19th June 2016, 10:00 am" -solved_by = 620 +solved_by = 626 difficulty_rating = "35%" content = """ Let σ(n) be the sum of the divisors of n. diff --git a/src/P566/problem.jl b/src/P566/problem.jl index 838523d..bf28b63 100644 --- a/src/P566/problem.jl +++ b/src/P566/problem.jl @@ -3,7 +3,7 @@ module Problem566 title = "Problem 566: Cake Icing Puzzle" published_on = "Saturday, 25th June 2016, 01:00 pm" -solved_by = 169 +solved_by = 170 difficulty_rating = "100%" content = """ Adam plays the following game with his birthday cake. diff --git a/src/P567/problem.jl b/src/P567/problem.jl index f3714cb..4fec72d 100644 --- a/src/P567/problem.jl +++ b/src/P567/problem.jl @@ -3,7 +3,7 @@ module Problem567 title = "Problem 567: Reciprocal games I" published_on = "Saturday, 3rd September 2016, 04:00 pm" -solved_by = 293 +solved_by = 295 difficulty_rating = "55%" content = """ Tom has built a random generator that is connected to a row of n light bulbs. Whenever the random generator is activated each of the n lights is turned on with the probability of \\frac 1 2, independently of its former state or the state of the other light bulbs. diff --git a/src/P568/problem.jl b/src/P568/problem.jl index 6b77d2b..7b36670 100644 --- a/src/P568/problem.jl +++ b/src/P568/problem.jl @@ -3,7 +3,7 @@ module Problem568 title = "Problem 568: Reciprocal games II" published_on = "Saturday, 3rd September 2016, 04:00 pm" -solved_by = 287 +solved_by = 289 difficulty_rating = "55%" content = """ Tom has built a random generator that is connected to a row of n light bulbs. Whenever the random generator is activated each of the n lights is turned on with the probability of \frac 1 2, independently of its former state or the state of the other light bulbs. diff --git a/src/P569/problem.jl b/src/P569/problem.jl index a6ed825..c7ebfac 100644 --- a/src/P569/problem.jl +++ b/src/P569/problem.jl @@ -3,7 +3,7 @@ module Problem569 title = "Problem 569: Prime Mountain Range" published_on = "Saturday, 10th September 2016, 07:00 pm" -solved_by = 400 +solved_by = 402 difficulty_rating = "45%" content = """ A diff --git a/src/P57/problem.jl b/src/P57/problem.jl index 5e5e6b2..b5f0614 100644 --- a/src/P57/problem.jl +++ b/src/P57/problem.jl @@ -3,7 +3,7 @@ module Problem57 title = "Problem 57: Square root convergents" published_on = "Friday, 21st November 2003, 06:00 pm" -solved_by = 43431 +solved_by = 43512 difficulty_rating = "5%" content = """ It is possible to show that the square root of two can be expressed as an infinite continued fraction. diff --git a/src/P570/problem.jl b/src/P570/problem.jl index 48084ee..8fc182a 100644 --- a/src/P570/problem.jl +++ b/src/P570/problem.jl @@ -3,7 +3,7 @@ module Problem570 title = "Problem 570: Snowflakes" published_on = "Saturday, 17th September 2016, 10:00 pm" -solved_by = 276 +solved_by = 278 difficulty_rating = "55%" content = """ A snowflake of order n is formed by overlaying an equilateral triangle (rotated by 180 degrees) onto each equilateral triangle of the same size in a snowflake of order n-1. A snowflake of order 1 is a single equilateral triangle. diff --git a/src/P571/problem.jl b/src/P571/problem.jl index d362e6a..0eb5a46 100644 --- a/src/P571/problem.jl +++ b/src/P571/problem.jl @@ -3,7 +3,7 @@ module Problem571 title = "Problem 571: Super Pandigital Numbers" published_on = "Sunday, 25th September 2016, 01:00 am" -solved_by = 1115 +solved_by = 1121 difficulty_rating = "25%" content = """ A positive number is \e[1mpandigital\e[0m in base b if it contains all digits from 0 to b - 1 at least once when written in base b. diff --git a/src/P572/problem.jl b/src/P572/problem.jl index bebf4fd..bf24b34 100644 --- a/src/P572/problem.jl +++ b/src/P572/problem.jl @@ -3,7 +3,7 @@ module Problem572 title = "Problem 572: Idempotent matrices" published_on = "Sunday, 2nd October 2016, 04:00 am" -solved_by = 335 +solved_by = 338 difficulty_rating = "50%" content = """ A matrix M is called idempotent if M² = M. diff --git a/src/P573/problem.jl b/src/P573/problem.jl index 4625b86..b20f2e8 100644 --- a/src/P573/problem.jl +++ b/src/P573/problem.jl @@ -3,7 +3,7 @@ module Problem573 title = "Problem 573: Unfair race" published_on = "Sunday, 9th October 2016, 07:00 am" -solved_by = 205 +solved_by = 206 difficulty_rating = "80%" content = """ n runners in very different training states want to compete in a race. Each one of them is given a different starting number k (1\\leq k \\leq n) according to the runner's (constant) individual racing speed being v_k=\\frac{k}{n}. diff --git a/src/P574/problem.jl b/src/P574/problem.jl index 74dc70f..642a60e 100644 --- a/src/P574/problem.jl +++ b/src/P574/problem.jl @@ -3,7 +3,7 @@ module Problem574 title = "Problem 574: Verifying Primes" published_on = "Sunday, 16th October 2016, 10:00 am" -solved_by = 265 +solved_by = 267 difficulty_rating = "50%" content = """ Let q be a prime and A ≥ B >0 be two integers with the following properties: diff --git a/src/P575/problem.jl b/src/P575/problem.jl index c118e8a..f614785 100644 --- a/src/P575/problem.jl +++ b/src/P575/problem.jl @@ -3,7 +3,7 @@ module Problem575 title = "Problem 575: Wandering Robots" published_on = "Saturday, 22nd October 2016, 01:00 pm" -solved_by = 591 +solved_by = 596 difficulty_rating = "35%" content = """ It was quite an ordinary day when a mysterious alien vessel appeared as if from nowhere. After waiting several hours and receiving no response it is decided to send a team to investigate, of which you are included. Upon entering the vessel you are met by a friendly holographic figure, Katharina, who explains the purpose of the vessel, Eulertopia. diff --git a/src/P576/problem.jl b/src/P576/problem.jl index 361c2f0..d506103 100644 --- a/src/P576/problem.jl +++ b/src/P576/problem.jl @@ -3,7 +3,7 @@ module Problem576 title = "Problem 576: Irrational jumps" published_on = "Saturday, 29th October 2016, 04:00 pm" -solved_by = 235 +solved_by = 236 difficulty_rating = "55%" content = """ diff --git a/src/P577/problem.jl b/src/P577/problem.jl index 961ec19..cbf28d0 100644 --- a/src/P577/problem.jl +++ b/src/P577/problem.jl @@ -3,7 +3,7 @@ module Problem577 title = "Problem 577: Counting hexagons" published_on = "Saturday, 12th November 2016, 07:00 pm" -solved_by = 1586 +solved_by = 1591 difficulty_rating = "20%" content = """ An equilateral triangle with integer side length n \\ge 3 is divided into n^2 equilateral triangles with side length 1 as shown in the diagram below. diff --git a/src/P578/problem.jl b/src/P578/problem.jl index 633739f..ef03c44 100644 --- a/src/P578/problem.jl +++ b/src/P578/problem.jl @@ -3,7 +3,7 @@ module Problem578 title = "Problem 578: Integers with decreasing prime powers" published_on = "Saturday, 19th November 2016, 10:00 pm" -solved_by = 230 +solved_by = 231 difficulty_rating = "80%" content = """ Any positive integer can be written as a product of prime powers: diff --git a/src/P58/problem.jl b/src/P58/problem.jl index 1a82e5c..13dc7b0 100644 --- a/src/P58/problem.jl +++ b/src/P58/problem.jl @@ -3,7 +3,7 @@ module Problem58 title = "Problem 58: Spiral primes" published_on = "Friday, 5th December 2003, 06:00 pm" -solved_by = 41924 +solved_by = 42012 difficulty_rating = "5%" content = """ Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. diff --git a/src/P580/problem.jl b/src/P580/problem.jl index 07b82db..714f0d5 100644 --- a/src/P580/problem.jl +++ b/src/P580/problem.jl @@ -3,7 +3,7 @@ module Problem580 title = "Problem 580: Squarefree Hilbert numbers" published_on = "Sunday, 4th December 2016, 04:00 am" -solved_by = 248 +solved_by = 250 difficulty_rating = "75%" content = """ A \e[1mHilbert number\e[0m is any positive integer of the form 4k+1 for integer k ≥ 0. We shall define a squarefree Hilbert number as diff --git a/src/P581/problem.jl b/src/P581/problem.jl index d43f993..e8825fd 100644 --- a/src/P581/problem.jl +++ b/src/P581/problem.jl @@ -3,7 +3,7 @@ module Problem581 title = "Problem 581: 47-smooth triangular numbers" published_on = "Sunday, 11th December 2016, 07:00 am" -solved_by = 860 +solved_by = 869 difficulty_rating = "30%" content = """ A number is p-smooth if it has no prime factors larger than p. diff --git a/src/P582/problem.jl b/src/P582/problem.jl index d8b8be5..af1edc4 100644 --- a/src/P582/problem.jl +++ b/src/P582/problem.jl @@ -3,7 +3,7 @@ module Problem582 title = "Problem 582: Nearly isosceles 120 degree triangles" published_on = "Sunday, 18th December 2016, 10:00 am" -solved_by = 323 +solved_by = 327 difficulty_rating = "50%" content = """ Let a, b and c be the sides of an integer sided triangle with one angle of 120 degrees, a≤b≤c and b-a≤100. diff --git a/src/P583/problem.jl b/src/P583/problem.jl index b502e70..5eeb7c3 100644 --- a/src/P583/problem.jl +++ b/src/P583/problem.jl @@ -3,7 +3,7 @@ module Problem583 title = "Problem 583: Heron Envelopes" published_on = "Saturday, 24th December 2016, 01:00 pm" -solved_by = 371 +solved_by = 372 difficulty_rating = "50%" content = """ diff --git a/src/P584/problem.jl b/src/P584/problem.jl index 1921883..d70e030 100644 --- a/src/P584/problem.jl +++ b/src/P584/problem.jl @@ -3,7 +3,7 @@ module Problem584 title = "Problem 584: Birthday Problem Revisited" published_on = "Saturday, 31st December 2016, 04:00 pm" -solved_by = 208 +solved_by = 209 difficulty_rating = "100%" content = """ A long long time ago in a galaxy far far away, the Wimwians, inhabitants of planet WimWi, discovered an unmanned drone that diff --git a/src/P585/problem.jl b/src/P585/problem.jl index 02803f0..1a2cc07 100644 --- a/src/P585/problem.jl +++ b/src/P585/problem.jl @@ -3,7 +3,7 @@ module Problem585 title = "Problem 585: Nested square roots" published_on = "Saturday, 7th January 2017, 07:00 pm" -solved_by = 173 +solved_by = 174 difficulty_rating = "100%" content = """ Consider the term \\small \\sqrt{x+\\sqrt{y}+\\sqrt{z}} that is representing a diff --git a/src/P586/problem.jl b/src/P586/problem.jl index 683134d..eb33e37 100644 --- a/src/P586/problem.jl +++ b/src/P586/problem.jl @@ -3,7 +3,7 @@ module Problem586 title = "Problem 586: Binary Quadratic Form" published_on = "Saturday, 14th January 2017, 10:00 pm" -solved_by = 234 +solved_by = 235 difficulty_rating = "75%" content = """ The number 209 can be expressed as a² + 3ab + b² in two distinct ways: diff --git a/src/P587/problem.jl b/src/P587/problem.jl index 452496e..287f9c4 100644 --- a/src/P587/problem.jl +++ b/src/P587/problem.jl @@ -3,7 +3,7 @@ module Problem587 title = "Problem 587: Concave triangle" published_on = "Sunday, 22nd January 2017, 01:00 am" -solved_by = 3148 +solved_by = 3161 difficulty_rating = "20%" content = """ diff --git a/src/P588/problem.jl b/src/P588/problem.jl index 6fb6a63..ee82765 100644 --- a/src/P588/problem.jl +++ b/src/P588/problem.jl @@ -3,7 +3,7 @@ module Problem588 title = "Problem 588: Quintinomial coefficients" published_on = "Sunday, 29th January 2017, 04:00 am" -solved_by = 441 +solved_by = 447 difficulty_rating = "40%" content = """ The coefficients in the expansion of (x+1)ᵏ are called \e[1mbinomial coefficients.\e[0m diff --git a/src/P59/problem.jl b/src/P59/problem.jl index c12b20f..b0184b9 100644 --- a/src/P59/problem.jl +++ b/src/P59/problem.jl @@ -3,7 +3,7 @@ module Problem59 title = "Problem 59: XOR decryption" published_on = "Friday, 19th December 2003, 06:00 pm" -solved_by = 42940 +solved_by = 43019 difficulty_rating = "5%" content = """ Each character on a computer is assigned a unique code and the preferred standard is ASCII (American Standard Code for diff --git a/src/P591/problem.jl b/src/P591/problem.jl index 0712f55..6be434c 100644 --- a/src/P591/problem.jl +++ b/src/P591/problem.jl @@ -3,7 +3,7 @@ module Problem591 title = "Problem 591: Best Approximations by Quadratic Integers" published_on = "Saturday, 18th February 2017, 01:00 pm" -solved_by = 196 +solved_by = 197 difficulty_rating = "95%" content = """ Given a non-square integer d, any real x can be approximated arbitrarily close by \e[1mquadratic integers\e[0m a + b√d, where a, b are diff --git a/src/P592/problem.jl b/src/P592/problem.jl index e08211d..e5b0c47 100644 --- a/src/P592/problem.jl +++ b/src/P592/problem.jl @@ -3,7 +3,7 @@ module Problem592 title = "Problem 592: Factorial trailing digits 2" published_on = "Saturday, 25th February 2017, 04:00 pm" -solved_by = 282 +solved_by = 284 difficulty_rating = "60%" content = """ For any N, let f(N) be the last twelve hexadecimal digits before the trailing zeroes in N!. diff --git a/src/P593/problem.jl b/src/P593/problem.jl index 0eeeb9b..36bd578 100644 --- a/src/P593/problem.jl +++ b/src/P593/problem.jl @@ -3,7 +3,7 @@ module Problem593 title = "Problem 593: Fleeting Medians" published_on = "Saturday, 4th March 2017, 07:00 pm" -solved_by = 539 +solved_by = 542 difficulty_rating = "35%" content = """ We define two sequences S = \\{S(1), S(2), ..., S(n)\\} and S_2 = \\{S_2(1), S_2(2), ..., S_2(n)\\}: diff --git a/src/P594/problem.jl b/src/P594/problem.jl index b4721fc..4c989ef 100644 --- a/src/P594/problem.jl +++ b/src/P594/problem.jl @@ -3,7 +3,7 @@ module Problem594 title = "Problem 594: Rhombus Tilings" published_on = "Saturday, 11th March 2017, 10:00 pm" -solved_by = 184 +solved_by = 185 difficulty_rating = "85%" content = """ diff --git a/src/P595/problem.jl b/src/P595/problem.jl index ec7758b..801a75c 100644 --- a/src/P595/problem.jl +++ b/src/P595/problem.jl @@ -3,7 +3,7 @@ module Problem595 title = "Problem 595: Incremental Random Sort" published_on = "Sunday, 19th March 2017, 01:00 am" -solved_by = 626 +solved_by = 628 difficulty_rating = "35%" content = """ A deck of cards numbered from 1 to n is shuffled randomly such that each permutation is equally likely. diff --git a/src/P596/problem.jl b/src/P596/problem.jl index d02adbb..2114eb1 100644 --- a/src/P596/problem.jl +++ b/src/P596/problem.jl @@ -3,7 +3,7 @@ module Problem596 title = "Problem 596: Number of lattice points in a hyperball" published_on = "Sunday, 26th March 2017, 04:00 am" -solved_by = 357 +solved_by = 362 difficulty_rating = "50%" content = """ Let T(r) be the number of integer quadruplets x, y, z, t such that x² + y² + z² + t² ≤ r². In other words, T(r) is the number of diff --git a/src/P597/problem.jl b/src/P597/problem.jl index e76e080..737dd4f 100644 --- a/src/P597/problem.jl +++ b/src/P597/problem.jl @@ -3,7 +3,7 @@ module Problem597 title = "Problem 597: Torpids" published_on = "Sunday, 2nd April 2017, 07:00 am" -solved_by = 170 +solved_by = 172 difficulty_rating = "100%" content = """ The Torpids are rowing races held annually in Oxford, following some curious rules: diff --git a/src/P598/problem.jl b/src/P598/problem.jl index ca4eaa6..e18dbd7 100644 --- a/src/P598/problem.jl +++ b/src/P598/problem.jl @@ -3,7 +3,7 @@ module Problem598 title = "Problem 598: Split Divisibilities" published_on = "Sunday, 9th April 2017, 10:00 am" -solved_by = 485 +solved_by = 487 difficulty_rating = "40%" content = """ Consider the number 48. diff --git a/src/P599/problem.jl b/src/P599/problem.jl index a7d16fe..36096d3 100644 --- a/src/P599/problem.jl +++ b/src/P599/problem.jl @@ -3,7 +3,7 @@ module Problem599 title = "Problem 599: Distinct Colourings of a Rubik's Cube" published_on = "Saturday, 15th April 2017, 01:00 pm" -solved_by = 301 +solved_by = 303 difficulty_rating = "60%" content = """ The well-known \e[1mRubik's Cube\e[0m puzzle has many fascinating mathematical properties. The 2×2×2 variant has 8 cubelets with a diff --git a/src/P6/problem.jl b/src/P6/problem.jl index 510bb67..286b168 100644 --- a/src/P6/problem.jl +++ b/src/P6/problem.jl @@ -3,7 +3,7 @@ module Problem6 title = "Problem 6: Sum square difference" published_on = "Friday, 14th December 2001, 06:00 pm" -solved_by = 500312 +solved_by = 500525 difficulty_rating = "5%" content = """ The sum of the squares of the first ten natural numbers is, diff --git a/src/P60/problem.jl b/src/P60/problem.jl index ef2f1df..08d7e4e 100644 --- a/src/P60/problem.jl +++ b/src/P60/problem.jl @@ -3,7 +3,7 @@ module Problem60 title = "Problem 60: Prime pair sets" published_on = "Friday, 2nd January 2004, 06:00 pm" -solved_by = 28112 +solved_by = 28175 difficulty_rating = "20%" content = """ The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result diff --git a/src/P600/problem.jl b/src/P600/problem.jl index 047b771..d5ed3e3 100644 --- a/src/P600/problem.jl +++ b/src/P600/problem.jl @@ -3,7 +3,7 @@ module Problem600 title = "Problem 600: Integer sided equiangular hexagons" published_on = "Saturday, 22nd April 2017, 04:00 pm" -solved_by = 614 +solved_by = 618 difficulty_rating = "35%" content = """ Let diff --git a/src/P601/problem.jl b/src/P601/problem.jl index 53f4cdb..50c880c 100644 --- a/src/P601/problem.jl +++ b/src/P601/problem.jl @@ -3,7 +3,7 @@ module Problem601 title = "Problem 601: Divisibility streaks" published_on = "Saturday, 29th April 2017, 07:00 pm" -solved_by = 2055 +solved_by = 2064 difficulty_rating = "20%" content = """ For every positive number n we define the function streak(n) = k as the smallest positive integer k such that n+k is not diff --git a/src/P602/problem.jl b/src/P602/problem.jl index 84a23ac..6d05b0f 100644 --- a/src/P602/problem.jl +++ b/src/P602/problem.jl @@ -3,7 +3,7 @@ module Problem602 title = "Problem 602: Product of Head Counts" published_on = "Saturday, 6th May 2017, 10:00 pm" -solved_by = 494 +solved_by = 497 difficulty_rating = "35%" content = """ Alice enlists the help of some friends to generate a random number, using a single unfair coin. She and her friends sit around a diff --git a/src/P603/problem.jl b/src/P603/problem.jl index a837d96..c637a7d 100644 --- a/src/P603/problem.jl +++ b/src/P603/problem.jl @@ -3,7 +3,7 @@ module Problem603 title = "Problem 603: Substring sums of prime concatenations" published_on = "Sunday, 14th May 2017, 01:00 am" -solved_by = 424 +solved_by = 429 difficulty_rating = "45%" content = """ Let S(n) be the sum of all contiguous integer-substrings that can be formed from the integer n. The substrings need not be diff --git a/src/P604/problem.jl b/src/P604/problem.jl index 7a196e2..9703bdf 100644 --- a/src/P604/problem.jl +++ b/src/P604/problem.jl @@ -3,7 +3,7 @@ module Problem604 title = "Problem 604: Convex path in square" published_on = "Sunday, 21st May 2017, 04:00 am" -solved_by = 504 +solved_by = 510 difficulty_rating = "40%" content = """ diff --git a/src/P605/problem.jl b/src/P605/problem.jl index c26b922..12e5d97 100644 --- a/src/P605/problem.jl +++ b/src/P605/problem.jl @@ -3,7 +3,7 @@ module Problem605 title = "Problem 605: Pairwise Coin-Tossing Game" published_on = "Sunday, 28th May 2017, 07:00 am" -solved_by = 851 +solved_by = 857 difficulty_rating = "25%" content = """ Consider an n-player game played in consecutive pairs: Round 1 takes place between players 1 and 2, round 2 takes place between players 2 and 3, and so on and so forth, all the way up to round n, which takes place between players n and 1. Then round n+1 takes place between players 1 and 2 as the entire cycle starts again. diff --git a/src/P606/problem.jl b/src/P606/problem.jl index 7609959..52d77c4 100644 --- a/src/P606/problem.jl +++ b/src/P606/problem.jl @@ -3,7 +3,7 @@ module Problem606 title = "Problem 606: Gozinta Chains II" published_on = "Sunday, 4th June 2017, 10:00 am" -solved_by = 378 +solved_by = 380 difficulty_rating = "50%" content = """ A \e[1mgozinta chain\e[0m for n is a sequence {1,a,b,...,n} where each element properly divides the next. diff --git a/src/P607/problem.jl b/src/P607/problem.jl index 1ed92af..4296dca 100644 --- a/src/P607/problem.jl +++ b/src/P607/problem.jl @@ -3,7 +3,7 @@ module Problem607 title = "Problem 607: Marsh Crossing" published_on = "Saturday, 10th June 2017, 01:00 pm" -solved_by = 1712 +solved_by = 1729 difficulty_rating = "20%" content = """ diff --git a/src/P608/problem.jl b/src/P608/problem.jl index c17a2b7..3e589cf 100644 --- a/src/P608/problem.jl +++ b/src/P608/problem.jl @@ -3,7 +3,7 @@ module Problem608 title = "Problem 608: Divisor Sums" published_on = "Saturday, 17th June 2017, 04:00 pm" -solved_by = 301 +solved_by = 305 difficulty_rating = "80%" content = """ Let D(m,n)=\\displaystyle\\sum_{d|m}\\sum_{k=1}^n\\sigma_{\\small 0}(kd) where d runs through all divisors of m and \\sigma_{\\small 0}(n) is the number of divisors of n. diff --git a/src/P609/problem.jl b/src/P609/problem.jl index 08f1303..d91b564 100644 --- a/src/P609/problem.jl +++ b/src/P609/problem.jl @@ -3,7 +3,7 @@ module Problem609 title = "Problem 609: π sequences" published_on = "Saturday, 9th September 2017, 04:00 pm" -solved_by = 932 +solved_by = 941 difficulty_rating = "20%" content = """ For every n ≥ 1 the \e[1mprime-counting\e[0m function π(n) is equal to the number of primes not exceeding n. diff --git a/src/P61/problem.jl b/src/P61/problem.jl index c1e089c..dbe153a 100644 --- a/src/P61/problem.jl +++ b/src/P61/problem.jl @@ -3,7 +3,7 @@ module Problem61 title = "Problem 61: Cyclical figurate numbers" published_on = "Friday, 16th January 2004, 06:00 pm" -solved_by = 26744 +solved_by = 26807 difficulty_rating = "20%" content = """ Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are diff --git a/src/P610/problem.jl b/src/P610/problem.jl index aaa6544..3b4eb3d 100644 --- a/src/P610/problem.jl +++ b/src/P610/problem.jl @@ -3,7 +3,7 @@ module Problem610 title = "Problem 610: Roman Numerals II" published_on = "Saturday, 23rd September 2017, 07:00 pm" -solved_by = 574 +solved_by = 580 difficulty_rating = "35%" content = """ A random generator produces a sequence of symbols drawn from the set {I, V, X, L, C, D, M, #}. Each item in the sequence is diff --git a/src/P611/problem.jl b/src/P611/problem.jl index a49c90b..3b402c7 100644 --- a/src/P611/problem.jl +++ b/src/P611/problem.jl @@ -3,7 +3,7 @@ module Problem611 title = "Problem 611: Hallway of square steps" published_on = "Saturday, 7th October 2017, 10:00 pm" -solved_by = 331 +solved_by = 333 difficulty_rating = "60%" content = """ Peter moves in a hallway with N+1 doors consecutively numbered from 0 through N. All doors are initially closed. Peter starts in diff --git a/src/P612/problem.jl b/src/P612/problem.jl index 6032a30..cbfdad3 100644 --- a/src/P612/problem.jl +++ b/src/P612/problem.jl @@ -3,7 +3,7 @@ module Problem612 title = "Problem 612: Friend numbers" published_on = "Sunday, 22nd October 2017, 01:00 am" -solved_by = 676 +solved_by = 681 difficulty_rating = "30%" content = """ Let's call two numbers friend numbers if their representation in base 10 has at least one common digit. diff --git a/src/P613/problem.jl b/src/P613/problem.jl index 282c4f0..9a80798 100644 --- a/src/P613/problem.jl +++ b/src/P613/problem.jl @@ -3,7 +3,7 @@ module Problem613 title = "Problem 613: Pythagorean Ant" published_on = "Sunday, 5th November 2017, 04:00 am" -solved_by = 1799 +solved_by = 1803 difficulty_rating = "20%" content = """ Dave is doing his homework on the balcony and, preparing a presentation about Pythagorean triangles, has just cut out a diff --git a/src/P614/problem.jl b/src/P614/problem.jl index 32064b5..b9416e6 100644 --- a/src/P614/problem.jl +++ b/src/P614/problem.jl @@ -3,7 +3,7 @@ module Problem614 title = "Problem 614: Special partitions 2" published_on = "Sunday, 19th November 2017, 07:00 am" -solved_by = 312 +solved_by = 313 difficulty_rating = "55%" content = """ An diff --git a/src/P615/problem.jl b/src/P615/problem.jl index 94c2f20..9651aae 100644 --- a/src/P615/problem.jl +++ b/src/P615/problem.jl @@ -3,7 +3,7 @@ module Problem615 title = "Problem 615: The millionth number with at least one million prime factors" published_on = "Sunday, 3rd December 2017, 10:00 am" -solved_by = 584 +solved_by = 587 difficulty_rating = "35%" content = """ Consider the natural numbers having at least 5 prime factors, which don't have to be distinct. diff --git a/src/P616/problem.jl b/src/P616/problem.jl index b0caf14..5fc827a 100644 --- a/src/P616/problem.jl +++ b/src/P616/problem.jl @@ -3,7 +3,7 @@ module Problem616 title = "Problem 616: Creative numbers" published_on = "Saturday, 16th December 2017, 01:00 pm" -solved_by = 481 +solved_by = 482 difficulty_rating = "40%" content = """ Alice plays the following game, she starts with a list of integers L and on each step she can either: diff --git a/src/P617/problem.jl b/src/P617/problem.jl index d414b53..b2fff95 100644 --- a/src/P617/problem.jl +++ b/src/P617/problem.jl @@ -3,7 +3,7 @@ module Problem617 title = "Problem 617: Mirror Power Sequence" published_on = "Saturday, 30th December 2017, 04:00 pm" -solved_by = 378 +solved_by = 379 difficulty_rating = "40%" content = """ For two integers n,e > 1, we define a (n,e)- diff --git a/src/P618/problem.jl b/src/P618/problem.jl index 119fed3..6b436bf 100644 --- a/src/P618/problem.jl +++ b/src/P618/problem.jl @@ -3,7 +3,7 @@ module Problem618 title = "Problem 618: Numbers with a given prime factor sum" published_on = "Saturday, 13th January 2018, 07:00 pm" -solved_by = 1040 +solved_by = 1046 difficulty_rating = "20%" content = """ Consider the numbers 15, 16 and 18: diff --git a/src/P619/problem.jl b/src/P619/problem.jl index b727cfc..18dd367 100644 --- a/src/P619/problem.jl +++ b/src/P619/problem.jl @@ -3,7 +3,7 @@ module Problem619 title = "Problem 619: Square subsets" published_on = "Saturday, 27th January 2018, 10:00 pm" -solved_by = 395 +solved_by = 400 difficulty_rating = "45%" content = """ For a set of positive integers {a, a+1, a+2, … , b}, let C(a,b) be the number of non-empty subsets in which the product of diff --git a/src/P62/problem.jl b/src/P62/problem.jl index 617a66d..4914d9c 100644 --- a/src/P62/problem.jl +++ b/src/P62/problem.jl @@ -3,7 +3,7 @@ module Problem62 title = "Problem 62: Cubic permutations" published_on = "Friday, 30th January 2004, 06:00 pm" -solved_by = 32965 +solved_by = 33030 difficulty_rating = "15%" content = """ The cube, 41063625 (345³), can be permuted to produce two other cubes: 56623104 (384³) and 66430125 (405³). In fact, diff --git a/src/P621/problem.jl b/src/P621/problem.jl index fe32d3e..e0b0b03 100644 --- a/src/P621/problem.jl +++ b/src/P621/problem.jl @@ -3,7 +3,7 @@ module Problem621 title = "Problem 621: Expressing an integer as the sum of triangular numbers" published_on = "Sunday, 25th February 2018, 04:00 am" -solved_by = 558 +solved_by = 561 difficulty_rating = "35%" content = """ Gauss famously proved that every positive integer can be expressed as the sum of three \e[1mtriangular numbers\e[0m (including 0 diff --git a/src/P622/problem.jl b/src/P622/problem.jl index 0df276d..2c69835 100644 --- a/src/P622/problem.jl +++ b/src/P622/problem.jl @@ -3,7 +3,7 @@ module Problem622 title = "Problem 622: Riffle Shuffles" published_on = "Sunday, 11th March 2018, 07:00 am" -solved_by = 1739 +solved_by = 1748 difficulty_rating = "15%" content = """ A riffle shuffle is executed as follows: a deck of cards is split into two equal halves, with the top half taken in the left hand and diff --git a/src/P623/problem.jl b/src/P623/problem.jl index 0d434e3..80965e8 100644 --- a/src/P623/problem.jl +++ b/src/P623/problem.jl @@ -3,7 +3,7 @@ module Problem623 title = "Problem 623: Lambda Count" published_on = "Sunday, 25th March 2018, 10:00 am" -solved_by = 319 +solved_by = 322 difficulty_rating = "45%" content = """ The lambda-calculus is a universal model of computation at the core of functional programming languages. It is based on diff --git a/src/P624/problem.jl b/src/P624/problem.jl index 2150036..03c2048 100644 --- a/src/P624/problem.jl +++ b/src/P624/problem.jl @@ -3,7 +3,7 @@ module Problem624 title = "Problem 624: Two heads are better than one" published_on = "Saturday, 7th April 2018, 01:00 pm" -solved_by = 626 +solved_by = 634 difficulty_rating = "30%" content = """ diff --git a/src/P625/problem.jl b/src/P625/problem.jl index 3a6de7c..f5a420f 100644 --- a/src/P625/problem.jl +++ b/src/P625/problem.jl @@ -3,7 +3,7 @@ module Problem625 title = "Problem 625: Gcd sum" published_on = "Saturday, 21st April 2018, 04:00 pm" -solved_by = 608 +solved_by = 615 difficulty_rating = "35%" content = """ G(N) = ∑ⱼ₌₁ᴺ ∑ᵢ₌₁ʲ gcd(i,j). diff --git a/src/P627/problem.jl b/src/P627/problem.jl index 4f72e28..86b564f 100644 --- a/src/P627/problem.jl +++ b/src/P627/problem.jl @@ -3,7 +3,7 @@ module Problem627 title = "Problem 627: Counting products" published_on = "Saturday, 19th May 2018, 10:00 pm" -solved_by = 238 +solved_by = 240 difficulty_rating = "60%" content = """ Consider the set S of all possible products of n positive integers not exceeding m, that is diff --git a/src/P628/problem.jl b/src/P628/problem.jl index 05fd2ac..38ab08c 100644 --- a/src/P628/problem.jl +++ b/src/P628/problem.jl @@ -3,7 +3,7 @@ module Problem628 title = "Problem 628: Open chess positions" published_on = "Sunday, 3rd June 2018, 01:00 am" -solved_by = 788 +solved_by = 796 difficulty_rating = "30%" content = """ diff --git a/src/P629/problem.jl b/src/P629/problem.jl index cf509bc..a3039ff 100644 --- a/src/P629/problem.jl +++ b/src/P629/problem.jl @@ -3,7 +3,7 @@ module Problem629 title = "Problem 629: Scatterstone Nim" published_on = "Sunday, 17th June 2018, 04:00 am" -solved_by = 238 +solved_by = 241 difficulty_rating = "55%" content = """ Alice and Bob are playing a modified game of Nim called Scatterstone Nim, with Alice going first, alternating turns with Bob. diff --git a/src/P63/problem.jl b/src/P63/problem.jl index 003761d..d3ec0fd 100644 --- a/src/P63/problem.jl +++ b/src/P63/problem.jl @@ -3,7 +3,7 @@ module Problem63 title = "Problem 63: Powerful digit counts" published_on = "Friday, 13th February 2004, 06:00 pm" -solved_by = 44923 +solved_by = 45012 difficulty_rating = "5%" content = """ The 5-digit number, 16807=7⁵, is also a fifth power. Similarly, the 9-digit number, 134217728=8⁹, is a ninth power. diff --git a/src/P630/problem.jl b/src/P630/problem.jl index af73a4d..c65a7b3 100644 --- a/src/P630/problem.jl +++ b/src/P630/problem.jl @@ -3,7 +3,7 @@ module Problem630 title = "Problem 630: Crossed lines" published_on = "Sunday, 1st July 2018, 07:00 am" -solved_by = 1000 +solved_by = 1006 difficulty_rating = "20%" content = """ Given a set, L, of unique lines, let M(L) be the number of lines in the set and let S(L) be the sum over every line of the number of times that line is crossed by another line in the set. For example, two sets of three lines are shown below: diff --git a/src/P631/problem.jl b/src/P631/problem.jl index c4baa40..d10b418 100644 --- a/src/P631/problem.jl +++ b/src/P631/problem.jl @@ -3,7 +3,7 @@ module Problem631 title = "Problem 631: Constrained Permutations" published_on = "Sunday, 15th July 2018, 10:00 am" -solved_by = 193 +solved_by = 194 difficulty_rating = "65%" content = """ Let (p₁p₂…pₖ) denote the permutation of the set 1, ..., k that maps pᵢ ↦ i. Define the length of the permutation to be k; diff --git a/src/P632/problem.jl b/src/P632/problem.jl index a5f015b..867d010 100644 --- a/src/P632/problem.jl +++ b/src/P632/problem.jl @@ -3,7 +3,7 @@ module Problem632 title = "Problem 632: Square prime factors" published_on = "Saturday, 28th July 2018, 01:00 pm" -solved_by = 473 +solved_by = 479 difficulty_rating = "35%" content = """ For an integer n, we define the square prime factors of n to be the primes whose square divides n. For example, the square diff --git a/src/P633/problem.jl b/src/P633/problem.jl index cb71737..87e233f 100644 --- a/src/P633/problem.jl +++ b/src/P633/problem.jl @@ -3,7 +3,7 @@ module Problem633 title = "Problem 633: Square prime factors II" published_on = "Saturday, 28th July 2018, 01:00 pm" -solved_by = 314 +solved_by = 317 difficulty_rating = "50%" content = """ For an integer n, we define the diff --git a/src/P634/problem.jl b/src/P634/problem.jl index e56bcc6..49c33b8 100644 --- a/src/P634/problem.jl +++ b/src/P634/problem.jl @@ -3,7 +3,7 @@ module Problem634 title = "Problem 634: Numbers of the form a²b³" published_on = "Saturday, 11th August 2018, 04:00 pm" -solved_by = 607 +solved_by = 611 difficulty_rating = "40%" content = """ Define F(n) to be the number of integers x ≤ n that can be written in the form x = a²b³, where a and b are integers not diff --git a/src/P635/problem.jl b/src/P635/problem.jl index aa2b03e..e625413 100644 --- a/src/P635/problem.jl +++ b/src/P635/problem.jl @@ -3,7 +3,7 @@ module Problem635 title = "Problem 635: Subset sums" published_on = "Saturday, 25th August 2018, 07:00 pm" -solved_by = 338 +solved_by = 341 difficulty_rating = "40%" content = """ Let A_q(n) be the number of subsets, B, of the set {1, 2, ..., q ⋅ n} that satisfy two conditions: diff --git a/src/P636/problem.jl b/src/P636/problem.jl index 1c9f5fb..ec284aa 100644 --- a/src/P636/problem.jl +++ b/src/P636/problem.jl @@ -3,7 +3,7 @@ module Problem636 title = "Problem 636: Restricted Factorisations" published_on = "Saturday, 8th September 2018, 10:00 pm" -solved_by = 189 +solved_by = 190 difficulty_rating = "90%" content = """ Consider writing a natural number as product of powers of natural numbers with given exponents, additionally requiring diff --git a/src/P637/problem.jl b/src/P637/problem.jl index 70e10f0..4280aa2 100644 --- a/src/P637/problem.jl +++ b/src/P637/problem.jl @@ -3,7 +3,7 @@ module Problem637 title = "Problem 637: Flexible digit sum" published_on = "Sunday, 23rd September 2018, 01:00 am" -solved_by = 319 +solved_by = 324 difficulty_rating = "45%" content = """ Given any positive integer n, we can construct a new integer by inserting plus signs between some of the digits of the base B diff --git a/src/P638/problem.jl b/src/P638/problem.jl index 11c6f55..16b16af 100644 --- a/src/P638/problem.jl +++ b/src/P638/problem.jl @@ -3,7 +3,7 @@ module Problem638 title = "Problem 638: Weighted lattice paths" published_on = "Sunday, 7th October 2018, 04:00 am" -solved_by = 371 +solved_by = 375 difficulty_rating = "40%" content = """ diff --git a/src/P639/problem.jl b/src/P639/problem.jl index 142df29..0303c61 100644 --- a/src/P639/problem.jl +++ b/src/P639/problem.jl @@ -3,7 +3,7 @@ module Problem639 title = "Problem 639: Summing a multiplicative function" published_on = "Sunday, 21st October 2018, 07:00 am" -solved_by = 259 +solved_by = 265 difficulty_rating = "70%" content = """ A diff --git a/src/P64/problem.jl b/src/P64/problem.jl index 695b11e..a89be10 100644 --- a/src/P64/problem.jl +++ b/src/P64/problem.jl @@ -3,7 +3,7 @@ module Problem64 title = "Problem 64: Odd period square roots" published_on = "Friday, 27th February 2004, 06:00 pm" -solved_by = 23227 +solved_by = 23276 difficulty_rating = "20%" content = """ All square roots are periodic when written as continued fractions and can be written in the form: diff --git a/src/P640/problem.jl b/src/P640/problem.jl index 948e48f..7021b90 100644 --- a/src/P640/problem.jl +++ b/src/P640/problem.jl @@ -3,7 +3,7 @@ module Problem640 title = "Problem 640: Shut the Box" published_on = "Sunday, 28th October 2018, 10:00 am" -solved_by = 341 +solved_by = 347 difficulty_rating = "50%" content = """ Bob plays a single-player game of chance using two standard 6-sided dice and twelve cards numbered 1 to 12. When the diff --git a/src/P641/problem.jl b/src/P641/problem.jl index c232f1d..43c5d59 100644 --- a/src/P641/problem.jl +++ b/src/P641/problem.jl @@ -3,7 +3,7 @@ module Problem641 title = "Problem 641: A Long Row of Dice" published_on = "Saturday, 3rd November 2018, 01:00 pm" -solved_by = 477 +solved_by = 483 difficulty_rating = "35%" content = """ Consider a row of n dice all showing 1. diff --git a/src/P642/problem.jl b/src/P642/problem.jl index 5048490..583cdb1 100644 --- a/src/P642/problem.jl +++ b/src/P642/problem.jl @@ -3,7 +3,7 @@ module Problem642 title = "Problem 642: Sum of largest prime factors" published_on = "Saturday, 10th November 2018, 04:00 pm" -solved_by = 352 +solved_by = 358 difficulty_rating = "45%" content = """ Let f(n) be the largest prime factor of n and \\displaystyle F(n) = \\sum_{i=2}^{n}f(i). diff --git a/src/P643/problem.jl b/src/P643/problem.jl index 5f55c04..44cfdff 100644 --- a/src/P643/problem.jl +++ b/src/P643/problem.jl @@ -3,7 +3,7 @@ module Problem643 title = "Problem 643: 2-Friendly" published_on = "Saturday, 17th November 2018, 07:00 pm" -solved_by = 591 +solved_by = 602 difficulty_rating = "25%" content = """ Two positive integers a and b are 2-friendly when gcd(a,b) = 2ᵗ, t > 0. For example, 24 and 40 are 2-friendly because diff --git a/src/P644/problem.jl b/src/P644/problem.jl index ce1b139..3781b72 100644 --- a/src/P644/problem.jl +++ b/src/P644/problem.jl @@ -3,7 +3,7 @@ module Problem644 title = "Problem 644: Squares on the line" published_on = "Saturday, 24th November 2018, 10:00 pm" -solved_by = 160 +solved_by = 161 difficulty_rating = "90%" content = """ Sam and Tom are trying a game of (partially) covering a given line segment of length L by taking turns in placing unit squares onto the line segment. diff --git a/src/P645/problem.jl b/src/P645/problem.jl index e20ad9f..86e43b5 100644 --- a/src/P645/problem.jl +++ b/src/P645/problem.jl @@ -3,7 +3,7 @@ module Problem645 title = "Problem 645: Every Day is a Holiday" published_on = "Sunday, 2nd December 2018, 01:00 am" -solved_by = 210 +solved_by = 215 difficulty_rating = "75%" content = """ On planet J, a year lasts for D days. Holidays are defined by the two following rules. diff --git a/src/P646/problem.jl b/src/P646/problem.jl index 456bdb7..0308a58 100644 --- a/src/P646/problem.jl +++ b/src/P646/problem.jl @@ -3,7 +3,7 @@ module Problem646 title = "Problem 646: Bounded Divisors" published_on = "Sunday, 9th December 2018, 04:00 am" -solved_by = 273 +solved_by = 278 difficulty_rating = "40%" content = """ diff --git a/src/P647/problem.jl b/src/P647/problem.jl index 1b9a008..5872a2c 100644 --- a/src/P647/problem.jl +++ b/src/P647/problem.jl @@ -3,7 +3,7 @@ module Problem647 title = "Problem 647: Linear Transformations of Polygonal Numbers" published_on = "Sunday, 16th December 2018, 07:00 am" -solved_by = 429 +solved_by = 439 difficulty_rating = "30%" content = """ diff --git a/src/P648/problem.jl b/src/P648/problem.jl index 76db1ad..d49ac42 100644 --- a/src/P648/problem.jl +++ b/src/P648/problem.jl @@ -3,7 +3,7 @@ module Problem648 title = "Problem 648: Skipping Squares" published_on = "Sunday, 23rd December 2018, 10:00 am" -solved_by = 281 +solved_by = 287 difficulty_rating = "45%" content = """ For some fixed ρ ∈ [0, 1], we begin a sum s at 0 and repeatedly apply a process: With probability ρ, we add 1 to s, otherwise diff --git a/src/P649/problem.jl b/src/P649/problem.jl index 98dfa1b..806e1d3 100644 --- a/src/P649/problem.jl +++ b/src/P649/problem.jl @@ -3,7 +3,7 @@ module Problem649 title = "Problem 649: Low-Prime Chessboard Nim" published_on = "Saturday, 29th December 2018, 01:00 pm" -solved_by = 401 +solved_by = 409 difficulty_rating = "30%" content = """ Alice and Bob are taking turns playing a game consisting of c different coins on a chessboard of size n by n. diff --git a/src/P65/problem.jl b/src/P65/problem.jl index 1b5de34..a1777b8 100644 --- a/src/P65/problem.jl +++ b/src/P65/problem.jl @@ -3,7 +3,7 @@ module Problem65 title = "Problem 65: Convergents of e" published_on = "Friday, 12th March 2004, 06:00 pm" -solved_by = 31182 +solved_by = 31256 difficulty_rating = "15%" content = """ The square root of 2 can be written as an infinite continued fraction. diff --git a/src/P650/problem.jl b/src/P650/problem.jl index b91f0a2..ae8aded 100644 --- a/src/P650/problem.jl +++ b/src/P650/problem.jl @@ -3,7 +3,7 @@ module Problem650 title = "Problem 650: Divisors of Binomial Product" published_on = "Saturday, 5th January 2019, 04:00 pm" -solved_by = 1618 +solved_by = 1631 difficulty_rating = "10%" content = """ diff --git a/src/P651/problem.jl b/src/P651/problem.jl index 607296c..9e01b97 100644 --- a/src/P651/problem.jl +++ b/src/P651/problem.jl @@ -3,7 +3,7 @@ module Problem651 title = "Problem 651: Patterned Cylinders" published_on = "Saturday, 12th January 2019, 07:00 pm" -solved_by = 167 +solved_by = 170 difficulty_rating = "70%" content = """ An infinitely long cylinder has its curved surface fully covered with different coloured but otherwise identical rectangular stickers, diff --git a/src/P652/problem.jl b/src/P652/problem.jl index aea6ee6..75a5e87 100644 --- a/src/P652/problem.jl +++ b/src/P652/problem.jl @@ -3,7 +3,7 @@ module Problem652 title = "Problem 652: Distinct values of a proto-logarithmic function" published_on = "Saturday, 19th January 2019, 10:00 pm" -solved_by = 165 +solved_by = 171 difficulty_rating = "70%" content = """ Consider the values of log₂(8), log₄(64) and log₃(27). All three are equal to 3. diff --git a/src/P653/problem.jl b/src/P653/problem.jl index add2c98..5f7e300 100644 --- a/src/P653/problem.jl +++ b/src/P653/problem.jl @@ -3,7 +3,7 @@ module Problem653 title = "Problem 653: Frictionless Tube" published_on = "Sunday, 27th January 2019, 01:00 am" -solved_by = 304 +solved_by = 310 difficulty_rating = "45%" content = """ Consider a horizontal frictionless tube with length L millimetres, and a diameter of 20 millimetres. The east end of the tube is diff --git a/src/P654/problem.jl b/src/P654/problem.jl index 68e811c..3c20623 100644 --- a/src/P654/problem.jl +++ b/src/P654/problem.jl @@ -3,7 +3,7 @@ module Problem654 title = "Problem 654: Neighbourly Constraints" published_on = "Sunday, 3rd February 2019, 04:00 am" -solved_by = 331 +solved_by = 337 difficulty_rating = "45%" content = """ Let T(n, m) be the number of m-tuples of positive integers such that the sum of any two neighbouring elements of the tuple is diff --git a/src/P655/problem.jl b/src/P655/problem.jl index 38ce427..217f152 100644 --- a/src/P655/problem.jl +++ b/src/P655/problem.jl @@ -3,7 +3,7 @@ module Problem655 title = "Problem 655: Divisible Palindromes" published_on = "Sunday, 10th February 2019, 07:00 am" -solved_by = 514 +solved_by = 524 difficulty_rating = "30%" content = """ The numbers 545, 5 995 and 15 151 are the three smallest \e[1mpalindromes\e[0m divisible by 109. There are nine palindromes less diff --git a/src/P656/problem.jl b/src/P656/problem.jl index 862326a..70cb320 100644 --- a/src/P656/problem.jl +++ b/src/P656/problem.jl @@ -3,7 +3,7 @@ module Problem656 title = "Problem 656: Palindromic sequences" published_on = "Sunday, 17th February 2019, 10:00 am" -solved_by = 235 +solved_by = 240 difficulty_rating = "50%" content = """ Given an irrational number α, let S_α(n) be the sequence S_α(n) = ⌊α ⋅ n⌋ - ⌊α ⋅ (n-1)⌋ for n ≥ 1. diff --git a/src/P657/problem.jl b/src/P657/problem.jl index 9c8b2cf..d929692 100644 --- a/src/P657/problem.jl +++ b/src/P657/problem.jl @@ -3,7 +3,7 @@ module Problem657 title = "Problem 657: Incomplete words" published_on = "Saturday, 23rd February 2019, 01:00 pm" -solved_by = 523 +solved_by = 532 difficulty_rating = "30%" content = """ In the context of formal languages, any finite sequence of letters of a given alphabet Σ is called a word over Σ. We call a diff --git a/src/P658/problem.jl b/src/P658/problem.jl index 8b53e68..a2e6471 100644 --- a/src/P658/problem.jl +++ b/src/P658/problem.jl @@ -3,7 +3,7 @@ module Problem658 title = "Problem 658: Incomplete words II" published_on = "Saturday, 23rd February 2019, 01:00 pm" -solved_by = 239 +solved_by = 244 difficulty_rating = "55%" content = """ In the context of diff --git a/src/P659/problem.jl b/src/P659/problem.jl index 527eb77..ad5d069 100644 --- a/src/P659/problem.jl +++ b/src/P659/problem.jl @@ -3,7 +3,7 @@ module Problem659 title = "Problem 659: Largest prime" published_on = "Saturday, 2nd March 2019, 04:00 pm" -solved_by = 912 +solved_by = 928 difficulty_rating = "20%" content = """ diff --git a/src/P66/problem.jl b/src/P66/problem.jl index ad38440..9095da8 100644 --- a/src/P66/problem.jl +++ b/src/P66/problem.jl @@ -3,7 +3,7 @@ module Problem66 title = "Problem 66: Diophantine equation" published_on = "Friday, 26th March 2004, 06:00 pm" -solved_by = 20658 +solved_by = 20716 difficulty_rating = "25%" content = """ Consider quadratic Diophantine equations of the form: diff --git a/src/P660/problem.jl b/src/P660/problem.jl index f5ea37f..852dcba 100644 --- a/src/P660/problem.jl +++ b/src/P660/problem.jl @@ -3,7 +3,7 @@ module Problem660 title = "Problem 660: Pandigital Triangles" published_on = "Saturday, 9th March 2019, 07:00 pm" -solved_by = 292 +solved_by = 297 difficulty_rating = "40%" content = """ We call an integer sided triangle n-pandigital if it contains one angle of 120 degrees and, when the sides of the triangle are diff --git a/src/P661/problem.jl b/src/P661/problem.jl index 85b6438..a78448a 100644 --- a/src/P661/problem.jl +++ b/src/P661/problem.jl @@ -3,7 +3,7 @@ module Problem661 title = "Problem 661: A Long Chess Match" published_on = "Saturday, 16th March 2019, 10:00 pm" -solved_by = 220 +solved_by = 223 difficulty_rating = "55%" content = """ Two friends A and B are great fans of Chess. They both enjoy playing the game, but after each game the player who lost the game would like to continue (to get back at the other player) and the player who won would prefer to stop (to finish on a high). diff --git a/src/P662/problem.jl b/src/P662/problem.jl index 43f54c9..2b9ebd0 100644 --- a/src/P662/problem.jl +++ b/src/P662/problem.jl @@ -3,7 +3,7 @@ module Problem662 title = "Problem 662: Fibonacci paths" published_on = "Sunday, 24th March 2019, 01:00 am" -solved_by = 782 +solved_by = 790 difficulty_rating = "25%" content = """ diff --git a/src/P663/problem.jl b/src/P663/problem.jl index 49b435d..2d3b8ec 100644 --- a/src/P663/problem.jl +++ b/src/P663/problem.jl @@ -3,7 +3,7 @@ module Problem663 title = "Problem 663: Sums of subarrays" published_on = "Sunday, 31st March 2019, 04:00 am" -solved_by = 352 +solved_by = 359 difficulty_rating = "35%" content = """ Let t_k be the diff --git a/src/P664/problem.jl b/src/P664/problem.jl index a34abdf..d339377 100644 --- a/src/P664/problem.jl +++ b/src/P664/problem.jl @@ -3,7 +3,7 @@ module Problem664 title = "Problem 664: An infinite game" published_on = "Sunday, 7th April 2019, 07:00 am" -solved_by = 188 +solved_by = 192 difficulty_rating = "65%" content = """ Peter is playing a solitaire game on an infinite checkerboard, each square of which can hold an unlimited number of tokens. diff --git a/src/P665/problem.jl b/src/P665/problem.jl index 539ba9f..868069f 100644 --- a/src/P665/problem.jl +++ b/src/P665/problem.jl @@ -3,7 +3,7 @@ module Problem665 title = "Problem 665: Proportionate Nim" published_on = "Sunday, 14th April 2019, 10:00 am" -solved_by = 252 +solved_by = 255 difficulty_rating = "55%" content = """ Two players play a game with two piles of stones, alternating turns. diff --git a/src/P666/problem.jl b/src/P666/problem.jl index 8b4dfe6..ec63e56 100644 --- a/src/P666/problem.jl +++ b/src/P666/problem.jl @@ -3,7 +3,7 @@ module Problem666 title = "Problem 666: Polymorphic Bacteria" published_on = "Saturday, 20th April 2019, 01:00 pm" -solved_by = 274 +solved_by = 276 difficulty_rating = "45%" content = """ Members of a species of bacteria occur in two different types: α and β. Individual bacteria are capable of multiplying and diff --git a/src/P667/problem.jl b/src/P667/problem.jl index fd98db9..0c918c2 100644 --- a/src/P667/problem.jl +++ b/src/P667/problem.jl @@ -3,7 +3,7 @@ module Problem667 title = "Problem 667: Moving Pentagon" published_on = "Saturday, 27th April 2019, 04:00 pm" -solved_by = 200 +solved_by = 202 difficulty_rating = "80%" content = """ diff --git a/src/P668/problem.jl b/src/P668/problem.jl index 0c571a4..04355d1 100644 --- a/src/P668/problem.jl +++ b/src/P668/problem.jl @@ -3,7 +3,7 @@ module Problem668 title = "Problem 668: Square root smooth Numbers" published_on = "Saturday, 4th May 2019, 07:00 pm" -solved_by = 1031 +solved_by = 1038 difficulty_rating = "20%" content = """ A positive integer is called square root smooth if all of its prime factors are strictly less than its square root. diff --git a/src/P669/problem.jl b/src/P669/problem.jl index a09d8f0..bce60ec 100644 --- a/src/P669/problem.jl +++ b/src/P669/problem.jl @@ -3,7 +3,7 @@ module Problem669 title = "Problem 669: The King's Banquet" published_on = "Saturday, 11th May 2019, 10:00 pm" -solved_by = 308 +solved_by = 312 difficulty_rating = "45%" content = """ The Knights of the Order of Fibonacci are preparing a grand feast for their king. There are n knights, and each knight is assigned a distinct number from 1 to n. diff --git a/src/P67/problem.jl b/src/P67/problem.jl index 9a37c4d..4a41b19 100644 --- a/src/P67/problem.jl +++ b/src/P67/problem.jl @@ -3,7 +3,7 @@ module Problem67 title = "Problem 67: Maximum path sum II" published_on = "Friday, 9th April 2004, 06:00 pm" -solved_by = 98817 +solved_by = 98948 difficulty_rating = "5%" content = """ By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to diff --git a/src/P670/problem.jl b/src/P670/problem.jl index 3cac3ef..a3eafaf 100644 --- a/src/P670/problem.jl +++ b/src/P670/problem.jl @@ -3,7 +3,7 @@ module Problem670 title = "Problem 670: Colouring a Strip" published_on = "Sunday, 19th May 2019, 01:00 am" -solved_by = 324 +solved_by = 328 difficulty_rating = "40%" content = """ A certain type of tile comes in three different sizes - 1×1, 1×2, and 1×3 - and in four different colours: blue, green, red and yellow. There is an unlimited number of tiles available in each combination of size and colour. diff --git a/src/P671/problem.jl b/src/P671/problem.jl index 9b41ab7..e0ba8af 100644 --- a/src/P671/problem.jl +++ b/src/P671/problem.jl @@ -3,7 +3,7 @@ module Problem671 title = "Problem 671: Colouring a Loop" published_on = "Sunday, 19th May 2019, 01:00 am" -solved_by = 163 +solved_by = 164 difficulty_rating = "80%" content = """ A certain type of flexible tile comes in three different sizes - 1×1, 1×2, and 1×3 - and in k different colours. There is an unlimited number of tiles available in each combination of size and colour. diff --git a/src/P672/problem.jl b/src/P672/problem.jl index f3ca803..3e3da3d 100644 --- a/src/P672/problem.jl +++ b/src/P672/problem.jl @@ -3,7 +3,7 @@ module Problem672 title = "Problem 672: One more one" published_on = "Sunday, 26th May 2019, 04:00 am" -solved_by = 268 +solved_by = 269 difficulty_rating = "50%" content = """ Consider the following process that can be applied recursively to any positive integer n: diff --git a/src/P673/problem.jl b/src/P673/problem.jl index 0039511..3aae1d9 100644 --- a/src/P673/problem.jl +++ b/src/P673/problem.jl @@ -3,7 +3,7 @@ module Problem673 title = "Problem 673: Beds and Desks" published_on = "Sunday, 2nd June 2019, 07:00 am" -solved_by = 313 +solved_by = 314 difficulty_rating = "35%" content = """ At Euler University, each of the n students (numbered from 1 to n) occupies a bed in the dormitory and uses a desk in the diff --git a/src/P675/problem.jl b/src/P675/problem.jl index c9d7621..9ff9825 100644 --- a/src/P675/problem.jl +++ b/src/P675/problem.jl @@ -3,7 +3,7 @@ module Problem675 title = "Problem 675: 2^{\\omega(n)}" published_on = "Saturday, 15th June 2019, 01:00 pm" -solved_by = 718 +solved_by = 731 difficulty_rating = "25%" content = """ diff --git a/src/P676/problem.jl b/src/P676/problem.jl index 6591b4e..70ef3bf 100644 --- a/src/P676/problem.jl +++ b/src/P676/problem.jl @@ -3,7 +3,7 @@ module Problem676 title = "Problem 676: Matching Digit Sums" published_on = "Saturday, 22nd June 2019, 04:00 pm" -solved_by = 229 +solved_by = 230 difficulty_rating = "50%" content = """ diff --git a/src/P677/problem.jl b/src/P677/problem.jl index a6de4b3..7e18031 100644 --- a/src/P677/problem.jl +++ b/src/P677/problem.jl @@ -3,7 +3,7 @@ module Problem677 title = "Problem 677: Coloured Graphs" published_on = "Saturday, 29th June 2019, 07:00 pm" -solved_by = 172 +solved_by = 174 difficulty_rating = "90%" content = """ Let g(n) be the number of \e[1mundirected graphs\e[0m with n nodes satisfying the following properties: diff --git a/src/P678/problem.jl b/src/P678/problem.jl index 60b2248..5e7e97a 100644 --- a/src/P678/problem.jl +++ b/src/P678/problem.jl @@ -3,7 +3,7 @@ module Problem678 title = "Problem 678: Fermat-like Equations" published_on = "Saturday, 7th September 2019, 10:00 pm" -solved_by = 229 +solved_by = 231 difficulty_rating = "55%" content = """ If a triple of positive integers (a, b, c) satisfies a² + b² = c², it is called a Pythagorean triple. No triple (a, b, c) satisfies diff --git a/src/P679/problem.jl b/src/P679/problem.jl index de50eae..0eb2220 100644 --- a/src/P679/problem.jl +++ b/src/P679/problem.jl @@ -3,7 +3,7 @@ module Problem679 title = "Problem 679: Freefarea" published_on = "Sunday, 15th September 2019, 01:00 am" -solved_by = 833 +solved_by = 848 difficulty_rating = "20%" content = """ Let S be the set consisting of the four letters \\{\\texttt{`A'},\\texttt{`E'},\\texttt{`F'},\\texttt{`R'}\\}. diff --git a/src/P68/problem.jl b/src/P68/problem.jl index a1e24f7..8f386d1 100644 --- a/src/P68/problem.jl +++ b/src/P68/problem.jl @@ -3,7 +3,7 @@ module Problem68 title = "Problem 68: Magic 5-gon ring" published_on = "Friday, 23rd April 2004, 06:00 pm" -solved_by = 21770 +solved_by = 21826 difficulty_rating = "25%" content = """ Consider the following "magic" 3-gon ring, filled with the numbers 1 to 6, and each line adding to nine. diff --git a/src/P681/problem.jl b/src/P681/problem.jl index a79226d..4b6811c 100644 --- a/src/P681/problem.jl +++ b/src/P681/problem.jl @@ -3,7 +3,7 @@ module Problem681 title = "Problem 681: Maximal Area" published_on = "Sunday, 29th September 2019, 07:00 am" -solved_by = 227 +solved_by = 228 difficulty_rating = "50%" content = """ Given positive integers a ≤ b ≤ c ≤ d, it may be possible to form quadrilaterals with edge lengths a,b,c,d (in any order). diff --git a/src/P682/problem.jl b/src/P682/problem.jl index dba6b63..f4bb7fb 100644 --- a/src/P682/problem.jl +++ b/src/P682/problem.jl @@ -3,7 +3,7 @@ module Problem682 title = "Problem 682: 5-Smooth Pairs" published_on = "Sunday, 6th October 2019, 10:00 am" -solved_by = 262 +solved_by = 267 difficulty_rating = "50%" content = """ 5-smooth numbers are numbers whose largest prime factor doesn't exceed 5. diff --git a/src/P683/problem.jl b/src/P683/problem.jl index c28c224..be017c9 100644 --- a/src/P683/problem.jl +++ b/src/P683/problem.jl @@ -3,7 +3,7 @@ module Problem683 title = "Problem 683: The Chase II" published_on = "Saturday, 12th October 2019, 01:00 pm" -solved_by = 319 +solved_by = 320 difficulty_rating = "40%" content = """ Consider the following variant of "The Chase" game. This game is played between n players sitting around a circular table diff --git a/src/P684/problem.jl b/src/P684/problem.jl index 838aea8..e5123a2 100644 --- a/src/P684/problem.jl +++ b/src/P684/problem.jl @@ -3,7 +3,7 @@ module Problem684 title = "Problem 684: Inverse Digit Sum" published_on = "Saturday, 19th October 2019, 04:00 pm" -solved_by = 2528 +solved_by = 2558 difficulty_rating = "5%" content = """ Define s(n) to be the smallest number that has a digit sum of n. For example s(10) = 19. diff --git a/src/P685/problem.jl b/src/P685/problem.jl index 4340633..cb0ecd0 100644 --- a/src/P685/problem.jl +++ b/src/P685/problem.jl @@ -3,7 +3,7 @@ module Problem685 title = "Problem 685: Inverse Digit Sum II" published_on = "Saturday, 19th October 2019, 04:00 pm" -solved_by = 192 +solved_by = 195 difficulty_rating = "65%" content = """ Writing down the numbers which have a digit sum of 10 in ascending order, we get: diff --git a/src/P686/problem.jl b/src/P686/problem.jl index 151bf47..b013a55 100644 --- a/src/P686/problem.jl +++ b/src/P686/problem.jl @@ -3,7 +3,7 @@ module Problem686 title = "Problem 686: Powers of Two" published_on = "Saturday, 26th October 2019, 07:00 pm" -solved_by = 3274 +solved_by = 3313 difficulty_rating = "5%" content = """ 2⁷ = 128 is the first power of two whose leading digits are "12". diff --git a/src/P687/problem.jl b/src/P687/problem.jl index 59b4d26..dd64aeb 100644 --- a/src/P687/problem.jl +++ b/src/P687/problem.jl @@ -3,7 +3,7 @@ module Problem687 title = "Problem 687: Shuffling Cards" published_on = "Saturday, 2nd November 2019, 10:00 pm" -solved_by = 297 +solved_by = 300 difficulty_rating = "45%" content = """ A standard deck of 52 playing cards, which consists of thirteen ranks (Ace, Two, ..., Ten, King, Queen and Jack) each in four suits (Clubs, Diamonds, Hearts and Spades), is randomly shuffled. Let us call a rank diff --git a/src/P688/problem.jl b/src/P688/problem.jl index f749cb1..ed337c0 100644 --- a/src/P688/problem.jl +++ b/src/P688/problem.jl @@ -3,7 +3,7 @@ module Problem688 title = "Problem 688: Piles of Plates" published_on = "Sunday, 10th November 2019, 01:00 am" -solved_by = 729 +solved_by = 737 difficulty_rating = "20%" content = """ diff --git a/src/P69/problem.jl b/src/P69/problem.jl index 1979e57..c7fe95f 100644 --- a/src/P69/problem.jl +++ b/src/P69/problem.jl @@ -3,7 +3,7 @@ module Problem69 title = "Problem 69: Totient maximum" published_on = "Friday, 7th May 2004, 06:00 pm" -solved_by = 36295 +solved_by = 36377 difficulty_rating = "10%" content = """ Euler's Totient function, ϕ(n) [sometimes called the phi function], is defined as the number of positive integers not exceeding n diff --git a/src/P690/problem.jl b/src/P690/problem.jl index 6902353..c62ace3 100644 --- a/src/P690/problem.jl +++ b/src/P690/problem.jl @@ -3,7 +3,7 @@ module Problem690 title = "Problem 690: Tom and Jerry" published_on = "Sunday, 24th November 2019, 07:00 am" -solved_by = 195 +solved_by = 198 difficulty_rating = "60%" content = """ Tom (the cat) and Jerry (the mouse) are playing on a simple graph G. diff --git a/src/P691/problem.jl b/src/P691/problem.jl index 66466d1..9134528 100644 --- a/src/P691/problem.jl +++ b/src/P691/problem.jl @@ -3,7 +3,7 @@ module Problem691 title = "Problem 691: Long substring with many repetitions" published_on = "Sunday, 1st December 2019, 10:00 am" -solved_by = 257 +solved_by = 261 difficulty_rating = "40%" content = """ Given a character string s, we define L(k,s) to be the length of the longest substring of s which appears at least k times in s, or 0 if such a substring does not exist. For example, L(3,\\text{“bbabcabcabcacba”})=4 because of the three occurrences of the substring \\text{“abca”}, and L(2,\\text{“bbabcabcabcacba”})=7 because of the repeated substring \\text{“abcabca”}. Note that the occurrences can overlap. diff --git a/src/P692/problem.jl b/src/P692/problem.jl index 78bbe13..db3aad8 100644 --- a/src/P692/problem.jl +++ b/src/P692/problem.jl @@ -3,7 +3,7 @@ module Problem692 title = "Problem 692: Siegbert and Jo" published_on = "Saturday, 7th December 2019, 01:00 pm" -solved_by = 1252 +solved_by = 1270 difficulty_rating = "10%" content = """ diff --git a/src/P693/problem.jl b/src/P693/problem.jl index fb23e8a..39bc29c 100644 --- a/src/P693/problem.jl +++ b/src/P693/problem.jl @@ -3,7 +3,7 @@ module Problem693 title = "Problem 693: Finite Sequence Generator" published_on = "Saturday, 14th December 2019, 04:00 pm" -solved_by = 279 +solved_by = 283 difficulty_rating = "40%" content = """ Two positive integers x and y (x > y) can generate a sequence in the following manner: diff --git a/src/P694/problem.jl b/src/P694/problem.jl index c26cb41..7cda21d 100644 --- a/src/P694/problem.jl +++ b/src/P694/problem.jl @@ -3,7 +3,7 @@ module Problem694 title = "Problem 694: Cube-full Divisors" published_on = "Saturday, 21st December 2019, 07:00 pm" -solved_by = 931 +solved_by = 940 difficulty_rating = "15%" content = """ diff --git a/src/P695/problem.jl b/src/P695/problem.jl index 9b13034..d9b983c 100644 --- a/src/P695/problem.jl +++ b/src/P695/problem.jl @@ -3,7 +3,7 @@ module Problem695 title = "Problem 695: Random Rectangles" published_on = "Saturday, 28th December 2019, 10:00 pm" -solved_by = 203 +solved_by = 205 difficulty_rating = "70%" content = """ Three points, P_1, P_2 and P_3, are randomly selected within a unit square. Consider the three rectangles with sides parallel to the sides of the unit square and a diagonal that is one of the three line segments \\overline{P_1P_2}, \\overline{P_1P_3} or \\overline{P_2P_3} (see picture below). diff --git a/src/P697/problem.jl b/src/P697/problem.jl index 1df7b87..cfd9f46 100644 --- a/src/P697/problem.jl +++ b/src/P697/problem.jl @@ -3,7 +3,7 @@ module Problem697 title = "Problem 697: Randomly Decaying Sequence" published_on = "Sunday, 12th January 2020, 04:00 am" -solved_by = 544 +solved_by = 552 difficulty_rating = "30%" content = """ Given a fixed real number c, define a random sequence (Xₙ)ₙ≥₀ by the following random process: diff --git a/src/P698/problem.jl b/src/P698/problem.jl index 66ec01e..ad390db 100644 --- a/src/P698/problem.jl +++ b/src/P698/problem.jl @@ -3,7 +3,7 @@ module Problem698 title = "Problem 698: 123 Numbers" published_on = "Sunday, 19th January 2020, 07:00 am" -solved_by = 415 +solved_by = 422 difficulty_rating = "30%" content = """ We define 123-numbers as follows: diff --git a/src/P699/problem.jl b/src/P699/problem.jl index 195ee7d..bed8dd6 100644 --- a/src/P699/problem.jl +++ b/src/P699/problem.jl @@ -3,7 +3,7 @@ module Problem699 title = "Problem 699: Triffle Numbers" published_on = "Sunday, 26th January 2020, 10:00 am" -solved_by = 180 +solved_by = 181 difficulty_rating = "80%" content = """ diff --git a/src/P7/problem.jl b/src/P7/problem.jl index 2ac6240..114cc70 100644 --- a/src/P7/problem.jl +++ b/src/P7/problem.jl @@ -3,7 +3,7 @@ module Problem7 title = "Problem 7: 10001st prime" published_on = "Friday, 28th December 2001, 06:00 pm" -solved_by = 428580 +solved_by = 428801 difficulty_rating = "5%" content = """ By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. diff --git a/src/P70/problem.jl b/src/P70/problem.jl index 60ff035..2aee776 100644 --- a/src/P70/problem.jl +++ b/src/P70/problem.jl @@ -3,7 +3,7 @@ module Problem70 title = "Problem 70: Totient permutation" published_on = "Friday, 21st May 2004, 06:00 pm" -solved_by = 23324 +solved_by = 23381 difficulty_rating = "20%" content = """ Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than diff --git a/src/P700/problem.jl b/src/P700/problem.jl index 1970ad5..2c466fa 100644 --- a/src/P700/problem.jl +++ b/src/P700/problem.jl @@ -3,7 +3,7 @@ module Problem700 title = "Problem 700: Eulercoin" published_on = "Saturday, 1st February 2020, 01:00 pm" -solved_by = 3058 +solved_by = 3108 difficulty_rating = "5%" content = """ Leonhard Euler was born on 15 April 1707. diff --git a/src/P701/problem.jl b/src/P701/problem.jl index 1ca3369..70816a6 100644 --- a/src/P701/problem.jl +++ b/src/P701/problem.jl @@ -3,7 +3,7 @@ module Problem701 title = "Problem 701: Random connected area" published_on = "Saturday, 8th February 2020, 04:00 pm" -solved_by = 327 +solved_by = 332 difficulty_rating = "40%" content = """ Consider a rectangle made up of W × H square cells each with area 1. diff --git a/src/P703/problem.jl b/src/P703/problem.jl index ec9cd51..923d3b7 100644 --- a/src/P703/problem.jl +++ b/src/P703/problem.jl @@ -3,7 +3,7 @@ module Problem703 title = "Problem 703: Circular Logic II" published_on = "Saturday, 22nd February 2020, 10:00 pm" -solved_by = 288 +solved_by = 292 difficulty_rating = "45%" content = """ Given an integer n, n ≥ 3, let B = {false,true} and let Bⁿ be the set of sequences of n values from B. The function f from diff --git a/src/P704/problem.jl b/src/P704/problem.jl index c9b47af..984502c 100644 --- a/src/P704/problem.jl +++ b/src/P704/problem.jl @@ -3,7 +3,7 @@ module Problem704 title = "Problem 704: Factors of Two in Binomial Coefficients" published_on = "Sunday, 1st March 2020, 01:00 am" -solved_by = 863 +solved_by = 873 difficulty_rating = "20%" content = """ diff --git a/src/P705/problem.jl b/src/P705/problem.jl index 548b50c..1cf718c 100644 --- a/src/P705/problem.jl +++ b/src/P705/problem.jl @@ -3,7 +3,7 @@ module Problem705 title = "Problem 705: Total Inversion Count of Divided Sequences" published_on = "Sunday, 8th March 2020, 04:00 am" -solved_by = 417 +solved_by = 422 difficulty_rating = "25%" content = """ The inversion count of a sequence of digits is the smallest number of adjacent pairs that must be swapped to sort the diff --git a/src/P706/problem.jl b/src/P706/problem.jl index edc4ecb..3f4d706 100644 --- a/src/P706/problem.jl +++ b/src/P706/problem.jl @@ -3,7 +3,7 @@ module Problem706 title = "Problem 706: 3-Like Numbers" published_on = "Sunday, 15th March 2020, 07:00 am" -solved_by = 525 +solved_by = 531 difficulty_rating = "20%" content = """ For a positive integer n, define f(n) to be the number of non-empty substrings of n that are divisible by 3. For example, diff --git a/src/P707/problem.jl b/src/P707/problem.jl index 6277655..1f9830b 100644 --- a/src/P707/problem.jl +++ b/src/P707/problem.jl @@ -3,7 +3,7 @@ module Problem707 title = "Problem 707: Lights Out" published_on = "Sunday, 22nd March 2020, 10:00 am" -solved_by = 220 +solved_by = 223 difficulty_rating = "55%" content = """ diff --git a/src/P708/problem.jl b/src/P708/problem.jl index ca1af85..74f5bc2 100644 --- a/src/P708/problem.jl +++ b/src/P708/problem.jl @@ -3,7 +3,7 @@ module Problem708 title = "Problem 708: Twos are all you need" published_on = "Saturday, 28th March 2020, 01:00 pm" -solved_by = 295 +solved_by = 297 difficulty_rating = "50%" content = """ A positive integer, n, is factorised into prime factors. We define f(n) to be the product when each prime factor is replaced with 2. In addition we define f(1)=1. diff --git a/src/P709/problem.jl b/src/P709/problem.jl index 7439883..822a1a9 100644 --- a/src/P709/problem.jl +++ b/src/P709/problem.jl @@ -3,7 +3,7 @@ module Problem709 title = "Problem 709: Even Stevens" published_on = "Saturday, 4th April 2020, 05:00 pm" -solved_by = 793 +solved_by = 803 difficulty_rating = "15%" content = """ Every day for the past n days Even Stevens brings home his groceries in a plastic bag. He stores these plastic bags in a diff --git a/src/P71/problem.jl b/src/P71/problem.jl index 8809b55..49748fb 100644 --- a/src/P71/problem.jl +++ b/src/P71/problem.jl @@ -3,7 +3,7 @@ module Problem71 title = "Problem 71: Ordered fractions" published_on = "Friday, 4th June 2004, 06:00 pm" -solved_by = 30556 +solved_by = 30624 difficulty_rating = "10%" content = """ Consider the fraction, n/d, where n and d are positive integers. If n 0. diff --git a/src/P719/problem.jl b/src/P719/problem.jl index 5507156..665ca9c 100644 --- a/src/P719/problem.jl +++ b/src/P719/problem.jl @@ -3,7 +3,7 @@ module Problem719 title = "Problem 719: Number Splitting" published_on = "Saturday, 6th June 2020, 08:00 pm" -solved_by = 3256 +solved_by = 3339 difficulty_rating = "5%" content = """ We define an S-number to be a natural number, n, that is a perfect square and its square root can be obtained by splitting the diff --git a/src/P72/problem.jl b/src/P72/problem.jl index 1b4a0dc..cf77b05 100644 --- a/src/P72/problem.jl +++ b/src/P72/problem.jl @@ -3,7 +3,7 @@ module Problem72 title = "Problem 72: Counting fractions" published_on = "Friday, 18th June 2004, 06:00 pm" -solved_by = 23384 +solved_by = 23439 difficulty_rating = "20%" content = """ Consider the fraction, n/d, where n and d are positive integers. If n0. Let S be the sum of the first n values of f. That is, diff --git a/src/P757/problem.jl b/src/P757/problem.jl index be6490e..f1b057d 100644 --- a/src/P757/problem.jl +++ b/src/P757/problem.jl @@ -3,7 +3,7 @@ module Problem757 title = "Problem 757: Stealthy Numbers" published_on = "Saturday, 15th May 2021, 05:00 pm" -solved_by = 1031 +solved_by = 1052 difficulty_rating = "10%" content = """ A positive integer N is stealthy, if there exist positive integers a, b, c, d such that ab = cd = N and a + b = c + d + 1. diff --git a/src/P758/problem.jl b/src/P758/problem.jl index 18db21b..0644091 100644 --- a/src/P758/problem.jl +++ b/src/P758/problem.jl @@ -3,7 +3,7 @@ module Problem758 title = "Problem 758: Buckets of Water" published_on = "Saturday, 29th May 2021, 08:00 pm" -solved_by = 217 +solved_by = 218 difficulty_rating = "50%" content = """ diff --git a/src/P759/problem.jl b/src/P759/problem.jl index 2fa4efd..b2e6ecc 100644 --- a/src/P759/problem.jl +++ b/src/P759/problem.jl @@ -3,7 +3,7 @@ module Problem759 title = "Problem 759: A squared recurrence relation" published_on = "Saturday, 12th June 2021, 11:00 pm" -solved_by = 489 +solved_by = 502 difficulty_rating = "25%" content = """ The function f is defined for all positive integers as follows: diff --git a/src/P76/problem.jl b/src/P76/problem.jl index f1024d9..ec8be77 100644 --- a/src/P76/problem.jl +++ b/src/P76/problem.jl @@ -3,7 +3,7 @@ module Problem76 title = "Problem 76: Counting summations" published_on = "Friday, 13th August 2004, 06:00 pm" -solved_by = 29737 +solved_by = 29805 difficulty_rating = "10%" content = """ It is possible to write five as a sum in exactly six different ways: diff --git a/src/P760/problem.jl b/src/P760/problem.jl index c79a28d..3bb0cb4 100644 --- a/src/P760/problem.jl +++ b/src/P760/problem.jl @@ -3,7 +3,7 @@ module Problem760 title = "Problem 760: Sum over Bitwise Operators" published_on = "Sunday, 27th June 2021, 02:00 am" -solved_by = 382 +solved_by = 388 difficulty_rating = "35%" content = """ Define diff --git a/src/P761/problem.jl b/src/P761/problem.jl index 9ba3233..9ca84c8 100644 --- a/src/P761/problem.jl +++ b/src/P761/problem.jl @@ -3,7 +3,7 @@ module Problem761 title = "Problem 761: Runner and Swimmer" published_on = "Sunday, 11th July 2021, 05:00 am" -solved_by = 142 +solved_by = 144 difficulty_rating = "90%" content = """ Two friends, a runner and a swimmer, are playing a sporting game: The swimmer is swimming within a circular pool while the diff --git a/src/P762/problem.jl b/src/P762/problem.jl index bfc7ad7..55bacb0 100644 --- a/src/P762/problem.jl +++ b/src/P762/problem.jl @@ -3,7 +3,7 @@ module Problem762 title = "Problem 762: Amoebas in a 2D grid" published_on = "Saturday, 4th September 2021, 02:00 pm" -solved_by = 183 +solved_by = 191 difficulty_rating = "50%" content = """ Consider a two dimensional grid of squares. The grid has 4 rows but infinitely many columns. diff --git a/src/P763/problem.jl b/src/P763/problem.jl index 8c97110..2786477 100644 --- a/src/P763/problem.jl +++ b/src/P763/problem.jl @@ -3,7 +3,7 @@ module Problem763 title = "Problem 763: Amoebas in a 3D grid" published_on = "Saturday, 4th September 2021, 02:00 pm" -solved_by = 71 +solved_by = 75 difficulty_rating = "100%" content = """ Consider a three dimensional grid of cubes. An amoeba in cube (x, y, z) can divide itself into three amoebas to occupy the diff --git a/src/P764/problem.jl b/src/P764/problem.jl index 2d026ec..eea95df 100644 --- a/src/P764/problem.jl +++ b/src/P764/problem.jl @@ -3,7 +3,7 @@ module Problem764 title = "Problem 764: Asymmetric Diophantine Equation" published_on = "Saturday, 11th September 2021, 05:00 pm" -solved_by = 321 +solved_by = 331 difficulty_rating = "40%" content = """ Consider the following Diophantine equation: diff --git a/src/P765/problem.jl b/src/P765/problem.jl index 3dd9a63..0b1abc0 100644 --- a/src/P765/problem.jl +++ b/src/P765/problem.jl @@ -3,7 +3,7 @@ module Problem765 title = "Problem 765: Trillionaire" published_on = "Saturday, 18th September 2021, 08:00 pm" -solved_by = 192 +solved_by = 197 difficulty_rating = "65%" content = """ Starting with 1 gram of gold you play a game. Each round you bet a certain amount of your gold: if you have x grams you can diff --git a/src/P766/problem.jl b/src/P766/problem.jl index a1c4be3..881457b 100644 --- a/src/P766/problem.jl +++ b/src/P766/problem.jl @@ -3,7 +3,7 @@ module Problem766 title = "Problem 766: Sliding Block Puzzle" published_on = "Saturday, 2nd October 2021, 11:00 pm" -solved_by = 291 +solved_by = 295 difficulty_rating = "35%" content = """ A diff --git a/src/P767/problem.jl b/src/P767/problem.jl index f285baf..9c0fa31 100644 --- a/src/P767/problem.jl +++ b/src/P767/problem.jl @@ -3,7 +3,7 @@ module Problem767 title = "Problem 767: Window into a Matrix II" published_on = "Sunday, 10th October 2021, 02:00 am" -solved_by = 162 +solved_by = 167 difficulty_rating = "60%" content = """ A window into a matrix is a contiguous sub matrix. diff --git a/src/P768/problem.jl b/src/P768/problem.jl index d926a68..48bc6c7 100644 --- a/src/P768/problem.jl +++ b/src/P768/problem.jl @@ -3,7 +3,7 @@ module Problem768 title = "Problem 768: Chandelier" published_on = "Sunday, 17th October 2021, 05:00 am" -solved_by = 138 +solved_by = 141 difficulty_rating = "95%" content = """ A certain type of chandelier contains a circular ring of n evenly spaced candleholders. diff --git a/src/P769/problem.jl b/src/P769/problem.jl index 490c39a..c8bb049 100644 --- a/src/P769/problem.jl +++ b/src/P769/problem.jl @@ -3,7 +3,7 @@ module Problem769 title = "Problem 769: Binary Quadratic Form II" published_on = "Sunday, 24th October 2021, 07:00 am" -solved_by = 127 +solved_by = 131 difficulty_rating = "90%" content = """ Consider the following binary quadratic form: diff --git a/src/P77/problem.jl b/src/P77/problem.jl index 81c76ef..9ebea51 100644 --- a/src/P77/problem.jl +++ b/src/P77/problem.jl @@ -3,7 +3,7 @@ module Problem77 title = "Problem 77: Prime summations" published_on = "Friday, 27th August 2004, 06:00 pm" -solved_by = 20081 +solved_by = 20133 difficulty_rating = "25%" content = """ It is possible to write ten as the sum of primes in exactly five different ways: diff --git a/src/P770/problem.jl b/src/P770/problem.jl index 7bc60f5..ddbb236 100644 --- a/src/P770/problem.jl +++ b/src/P770/problem.jl @@ -3,7 +3,7 @@ module Problem770 title = "Problem 770: Delphi Flip" published_on = "Sunday, 31st October 2021, 10:00 am" -solved_by = 457 +solved_by = 467 difficulty_rating = "30%" content = """ A and B play a game. A has originally 1 gram of gold and B has an unlimited amount. Each round goes as follows: diff --git a/src/P771/problem.jl b/src/P771/problem.jl index 2d51de1..0bc2029 100644 --- a/src/P771/problem.jl +++ b/src/P771/problem.jl @@ -3,7 +3,7 @@ module Problem771 title = "Problem 771: Pseudo Geometric Sequences" published_on = "Saturday, 6th November 2021, 01:00 pm" -solved_by = 119 +solved_by = 123 difficulty_rating = "80%" content = """ We define a pseudo-geometric sequence to be a finite sequence a₀, a₁, …, aₙ of positive integers, satisfying the following diff --git a/src/P772/problem.jl b/src/P772/problem.jl index ed04ef8..e373af0 100644 --- a/src/P772/problem.jl +++ b/src/P772/problem.jl @@ -3,7 +3,7 @@ module Problem772 title = "Problem 772: Balanceable k-bounded partitions" published_on = "Saturday, 13th November 2021, 04:00 pm" -solved_by = 438 +solved_by = 445 difficulty_rating = "20%" content = """ A k-bounded partition of a positive integer N is a way of writing N as a sum of positive integers not exceeding k. diff --git a/src/P773/problem.jl b/src/P773/problem.jl index e09d9c0..6c8276e 100644 --- a/src/P773/problem.jl +++ b/src/P773/problem.jl @@ -3,7 +3,7 @@ module Problem773 title = "Problem 773: Ruff Numbers" published_on = "Saturday, 20th November 2021, 07:00 pm" -solved_by = 184 +solved_by = 188 difficulty_rating = "50%" content = """ Let Sₖ be the set containing 2 and 5 and the first k primes that end in 7. For example, S₃ = {2,5,7,17,37}. diff --git a/src/P774/problem.jl b/src/P774/problem.jl index c0986bb..08c5bbd 100644 --- a/src/P774/problem.jl +++ b/src/P774/problem.jl @@ -3,7 +3,7 @@ module Problem774 title = "Problem 774: Conjunctive Sequences" published_on = "Saturday, 27th November 2021, 10:00 pm" -solved_by = 118 +solved_by = 123 difficulty_rating = "90%" content = """ Let & denote the bitwise AND operation. diff --git a/src/P775/problem.jl b/src/P775/problem.jl index 7e603b6..200d867 100644 --- a/src/P775/problem.jl +++ b/src/P775/problem.jl @@ -3,7 +3,7 @@ module Problem775 title = "Problem 775: Saving Paper" published_on = "Sunday, 5th December 2021, 01:00 am" -solved_by = 222 +solved_by = 227 difficulty_rating = "40%" content = """ When wrapping several cubes in paper, it is more efficient to wrap them all together than to wrap each one individually. For example, with 10 cubes of unit edge length, it would take 30 units of paper to wrap them in the arrangement shown below, but 60 units to wrap them separately. diff --git a/src/P776/problem.jl b/src/P776/problem.jl index 8716645..aa9ad75 100644 --- a/src/P776/problem.jl +++ b/src/P776/problem.jl @@ -3,7 +3,7 @@ module Problem776 title = "Problem 776: Digit Sum Division" published_on = "Sunday, 12th December 2021, 04:00 am" -solved_by = 475 +solved_by = 487 difficulty_rating = "25%" content = """ diff --git a/src/P777/problem.jl b/src/P777/problem.jl index b895249..3780abd 100644 --- a/src/P777/problem.jl +++ b/src/P777/problem.jl @@ -3,7 +3,7 @@ module Problem777 title = "Problem 777: Lissajous Curves" published_on = "Sunday, 19th December 2021, 07:00 am" -solved_by = 110 +solved_by = 112 difficulty_rating = "95%" content = """ For coprime positive integers a and b, let C_{a,b} be the curve defined by: diff --git a/src/P778/problem.jl b/src/P778/problem.jl index 06eba64..1b7aad3 100644 --- a/src/P778/problem.jl +++ b/src/P778/problem.jl @@ -3,7 +3,7 @@ module Problem778 title = "Problem 778: Freshman's Product" published_on = "Sunday, 26th December 2021, 10:00 am" -solved_by = 353 +solved_by = 361 difficulty_rating = "30%" content = """ If a,b are two nonnegative integers with decimal representations a = (…a₂a₁a₀) and b = (…b₂b₁b₀) respectively, then the diff --git a/src/P779/problem.jl b/src/P779/problem.jl index 134461d..ce09e98 100644 --- a/src/P779/problem.jl +++ b/src/P779/problem.jl @@ -3,7 +3,7 @@ module Problem779 title = "Problem 779: Prime Factor and Exponent" published_on = "Saturday, 1st January 2022, 01:00 pm" -solved_by = 430 +solved_by = 435 difficulty_rating = "25%" content = """ diff --git a/src/P78/problem.jl b/src/P78/problem.jl index 10ce24f..a19d337 100644 --- a/src/P78/problem.jl +++ b/src/P78/problem.jl @@ -3,7 +3,7 @@ module Problem78 title = "Problem 78: Coin partitions" published_on = "Friday, 10th September 2004, 06:00 pm" -solved_by = 17728 +solved_by = 17781 difficulty_rating = "30%" content = """ Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be diff --git a/src/P780/problem.jl b/src/P780/problem.jl index 54e1ae5..3e0cbd1 100644 --- a/src/P780/problem.jl +++ b/src/P780/problem.jl @@ -3,7 +3,7 @@ module Problem780 title = "Problem 780: Toriangulations" published_on = "Saturday, 8th January 2022, 04:00 pm" -solved_by = 67 +solved_by = 70 difficulty_rating = "100%" content = """ For positive real numbers a,b, an a\\times b diff --git a/src/P781/problem.jl b/src/P781/problem.jl index 0a41666..13f1009 100644 --- a/src/P781/problem.jl +++ b/src/P781/problem.jl @@ -3,7 +3,7 @@ module Problem781 title = "Problem 781: Feynman Diagrams" published_on = "Saturday, 15th January 2022, 07:00 pm" -solved_by = 117 +solved_by = 118 difficulty_rating = "95%" content = """ Let F(n) be the number of connected graphs with blue edges (directed) and red edges (undirected) containing: diff --git a/src/P783/problem.jl b/src/P783/problem.jl index 29615e6..446654f 100644 --- a/src/P783/problem.jl +++ b/src/P783/problem.jl @@ -3,7 +3,7 @@ module Problem783 title = "Problem 783: Urns" published_on = "Sunday, 30th January 2022, 01:00 am" -solved_by = 183 +solved_by = 185 difficulty_rating = "50%" content = """ diff --git a/src/P784/problem.jl b/src/P784/problem.jl index 9fbc97a..4c324c5 100644 --- a/src/P784/problem.jl +++ b/src/P784/problem.jl @@ -3,7 +3,7 @@ module Problem784 title = "Problem 784: Reciprocal Pairs" published_on = "Sunday, 6th February 2022, 04:00 am" -solved_by = 347 +solved_by = 357 difficulty_rating = "30%" content = """ diff --git a/src/P785/problem.jl b/src/P785/problem.jl index be7bee5..12e93e7 100644 --- a/src/P785/problem.jl +++ b/src/P785/problem.jl @@ -3,7 +3,7 @@ module Problem785 title = "Problem 785: Symmetric Diophantine equation" published_on = "Sunday, 13th February 2022, 07:00 am" -solved_by = 175 +solved_by = 178 difficulty_rating = "55%" content = """ Consider the following Diophantine equation: diff --git a/src/P786/problem.jl b/src/P786/problem.jl index 28751bf..c7e23d8 100644 --- a/src/P786/problem.jl +++ b/src/P786/problem.jl @@ -3,7 +3,7 @@ module Problem786 title = "Problem 786: Billiard" published_on = "Sunday, 20th February 2022, 10:00 am" -solved_by = 110 +solved_by = 113 difficulty_rating = "95%" content = """ diff --git a/src/P787/problem.jl b/src/P787/problem.jl index 43fff04..b99778b 100644 --- a/src/P787/problem.jl +++ b/src/P787/problem.jl @@ -3,7 +3,7 @@ module Problem787 title = "Problem 787: Bézout's Game" published_on = "Saturday, 26th February 2022, 01:00 pm" -solved_by = 181 +solved_by = 184 difficulty_rating = "40%" content = """ Two players play a game with two piles of stones. They take alternating turns. If there are currently a stones in the first pile and diff --git a/src/P788/problem.jl b/src/P788/problem.jl index 591a888..5d180f8 100644 --- a/src/P788/problem.jl +++ b/src/P788/problem.jl @@ -3,7 +3,7 @@ module Problem788 title = "Problem 788: Dominating Numbers" published_on = "Saturday, 5th March 2022, 04:00 pm" -solved_by = 912 +solved_by = 930 difficulty_rating = "10%" content = """ A dominating number is a positive integer that has more than half of its digits equal. diff --git a/src/P789/problem.jl b/src/P789/problem.jl index 4104572..7b67b80 100644 --- a/src/P789/problem.jl +++ b/src/P789/problem.jl @@ -3,7 +3,7 @@ module Problem789 title = "Problem 789: Minimal pairing modulo p" published_on = "Saturday, 12th March 2022, 07:00 pm" -solved_by = 171 +solved_by = 174 difficulty_rating = "50%" content = """ Given an odd prime p, put the numbers 1,...,p-1 into \\frac{p-1}{2} pairs such that each number appears exactly once. Each pair (a,b) has a cost of ab \\bmod p. For example, if p=5 the pair (3,4) has a cost of 12 \\bmod 5 = 2. diff --git a/src/P79/problem.jl b/src/P79/problem.jl index e9e2e92..b6a6f17 100644 --- a/src/P79/problem.jl +++ b/src/P79/problem.jl @@ -3,7 +3,7 @@ module Problem79 title = "Problem 79: Passcode derivation" published_on = "Friday, 17th September 2004, 06:00 pm" -solved_by = 42413 +solved_by = 42486 difficulty_rating = "5%" content = """ A common security method used for online banking is to ask the user for three random characters from a passcode. For diff --git a/src/P790/problem.jl b/src/P790/problem.jl index 8476a93..1f3ca63 100644 --- a/src/P790/problem.jl +++ b/src/P790/problem.jl @@ -3,7 +3,7 @@ module Problem790 title = "Problem 790: Clock Grid" published_on = "Saturday, 19th March 2022, 10:00 pm" -solved_by = 239 +solved_by = 242 difficulty_rating = "45%" content = """ There is a grid of length and width 50515093 points. A clock is placed on each grid point. The clocks are all analogue showing diff --git a/src/P791/problem.jl b/src/P791/problem.jl index e3e815e..b6c3d3c 100644 --- a/src/P791/problem.jl +++ b/src/P791/problem.jl @@ -3,7 +3,7 @@ module Problem791 title = "Problem 791: Average and Variance" published_on = "Sunday, 27th March 2022, 02:00 am" -solved_by = 148 +solved_by = 150 difficulty_rating = "60%" content = """ Denote the average of k numbers x_1, ..., x_k by \\bar{x} = \\frac{1}{k} \\sum_i x_i. Their variance is defined as \\frac{1}{k} \\sum_i \\left( x_i - \\bar{x} \\right) ^ 2. diff --git a/src/P792/problem.jl b/src/P792/problem.jl index 4f6f1b0..b478887 100644 --- a/src/P792/problem.jl +++ b/src/P792/problem.jl @@ -3,7 +3,7 @@ module Problem792 title = "Problem 792: Too Many Twos" published_on = "Sunday, 3rd April 2022, 05:00 am" -solved_by = 105 +solved_by = 111 difficulty_rating = "100%" content = """ We define \\nu_2(n) to be the largest integer r such that 2^r divides n. For example, \\nu_2(24) = 3. diff --git a/src/P793/problem.jl b/src/P793/problem.jl index 6025f30..eac7852 100644 --- a/src/P793/problem.jl +++ b/src/P793/problem.jl @@ -3,7 +3,7 @@ module Problem793 title = "Problem 793: Median of Products" published_on = "Sunday, 10th April 2022, 08:00 am" -solved_by = 563 +solved_by = 573 difficulty_rating = "20%" content = """ Let Sᵢ be an integer sequence produced with the following pseudo-random number generator: diff --git a/src/P794/problem.jl b/src/P794/problem.jl index def3706..6ef55e4 100644 --- a/src/P794/problem.jl +++ b/src/P794/problem.jl @@ -3,7 +3,7 @@ module Problem794 title = "Problem 794: Seventeen Points" published_on = "Sunday, 17th April 2022, 11:00 am" -solved_by = 280 +solved_by = 285 difficulty_rating = "35%" content = """ This problem uses half open interval notation where [a,b) represents a \\le x < b. diff --git a/src/P795/problem.jl b/src/P795/problem.jl index 6829ba5..aac8604 100644 --- a/src/P795/problem.jl +++ b/src/P795/problem.jl @@ -3,7 +3,7 @@ module Problem795 title = "Problem 795: Alternating GCD Sum" published_on = "Saturday, 23rd April 2022, 02:00 pm" -solved_by = 287 +solved_by = 302 difficulty_rating = "30%" content = """ diff --git a/src/P796/problem.jl b/src/P796/problem.jl index abb8f46..4fe16cc 100644 --- a/src/P796/problem.jl +++ b/src/P796/problem.jl @@ -3,7 +3,7 @@ module Problem796 title = "Problem 796: A Grand Shuffle" published_on = "Saturday, 30th April 2022, 05:00 pm" -solved_by = 182 +solved_by = 187 difficulty_rating = "55%" content = """ A standard 52 card deck comprises thirteen ranks in four suits. However, modern decks have two additional Jokers, which diff --git a/src/P797/problem.jl b/src/P797/problem.jl index 0e2834a..5147061 100644 --- a/src/P797/problem.jl +++ b/src/P797/problem.jl @@ -3,7 +3,7 @@ module Problem797 title = "Problem 797: Cyclogenic Polynomials" published_on = "Saturday, 7th May 2022, 08:00 pm" -solved_by = 169 +solved_by = 177 difficulty_rating = "50%" content = """ A diff --git a/src/P798/problem.jl b/src/P798/problem.jl index 2ebb14a..3a1541c 100644 --- a/src/P798/problem.jl +++ b/src/P798/problem.jl @@ -3,7 +3,7 @@ module Problem798 title = "Problem 798: Card Stacking Game" published_on = "Saturday, 14th May 2022, 11:00 pm" -solved_by = 99 +solved_by = 103 difficulty_rating = "100%" content = """ Two players play a game with a deck of cards which contains s suits with each suit containing n cards numbered from 1 to n. diff --git a/src/P799/problem.jl b/src/P799/problem.jl index 9276c4e..24805dd 100644 --- a/src/P799/problem.jl +++ b/src/P799/problem.jl @@ -3,7 +3,7 @@ module Problem799 title = "Problem 799: Pentagonal Puzzle" published_on = "Sunday, 22nd May 2022, 02:00 am" -solved_by = 205 +solved_by = 210 difficulty_rating = "50%" content = """ diff --git a/src/P8/problem.jl b/src/P8/problem.jl index 7d1acc1..b729a68 100644 --- a/src/P8/problem.jl +++ b/src/P8/problem.jl @@ -3,7 +3,7 @@ module Problem8 title = "Problem 8: Largest product in a series" published_on = "Friday, 11th January 2002, 06:00 pm" -solved_by = 359581 +solved_by = 359817 difficulty_rating = "5%" content = """ The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832. diff --git a/src/P80/problem.jl b/src/P80/problem.jl index 1a58076..fa1c081 100644 --- a/src/P80/problem.jl +++ b/src/P80/problem.jl @@ -3,7 +3,7 @@ module Problem80 title = "Problem 80: Square root digital expansion" published_on = "Friday, 8th October 2004, 06:00 pm" -solved_by = 20725 +solved_by = 20780 difficulty_rating = "20%" content = """ It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such diff --git a/src/P800/problem.jl b/src/P800/problem.jl index ff10798..1189561 100644 --- a/src/P800/problem.jl +++ b/src/P800/problem.jl @@ -3,7 +3,7 @@ module Problem800 title = "Problem 800: Hybrid Integers" published_on = "Sunday, 29th May 2022, 05:00 am" -solved_by = 1307 +solved_by = 1364 difficulty_rating = "5%" content = """ An integer of the form p^q q^p with prime numbers p ≠ q is called a hybrid-integer. diff --git a/src/P801/problem.jl b/src/P801/problem.jl index 78b395f..d5e1aff 100644 --- a/src/P801/problem.jl +++ b/src/P801/problem.jl @@ -3,7 +3,7 @@ module Problem801 title = "Problem 801: xʸ ≡ yˣ" published_on = "Sunday, 5th June 2022, 08:00 am" -solved_by = 223 +solved_by = 229 difficulty_rating = "50%" content = """ The positive integral solutions of the equation xʸ = yˣ are (2,4), (4,2) and (k,k) for all k > 0. diff --git a/src/P802/problem.jl b/src/P802/problem.jl index 5630b32..256d6b0 100644 --- a/src/P802/problem.jl +++ b/src/P802/problem.jl @@ -3,7 +3,7 @@ module Problem802 title = "Problem 802: Iterated Composition" published_on = "Sunday, 12th June 2022, 11:00 am" -solved_by = 212 +solved_by = 218 difficulty_rating = "35%" content = """ Let R² be the set of pairs of real numbers (x, y). Let π = 3.14159⋯. diff --git a/src/P803/problem.jl b/src/P803/problem.jl index 1b4eeb8..e6fa54e 100644 --- a/src/P803/problem.jl +++ b/src/P803/problem.jl @@ -3,7 +3,7 @@ module Problem803 title = "Problem 803: Pseudorandom sequence" published_on = "Saturday, 18th June 2022, 02:00 pm" -solved_by = 193 +solved_by = 198 difficulty_rating = "55%" content = """ \e[1mRand48\e[0m is a pseudorandom number generator used by some programming languages. It generates a sequence from any given diff --git a/src/P804/problem.jl b/src/P804/problem.jl index 0e68cec..f6c2000 100644 --- a/src/P804/problem.jl +++ b/src/P804/problem.jl @@ -3,7 +3,7 @@ module Problem804 title = "Problem 804: Counting Binary Quadratic Representations" published_on = "Saturday, 25th June 2022, 05:00 pm" -solved_by = 549 +solved_by = 563 difficulty_rating = "20%" content = """ Let g(n) denote the number of ways a positive integer n can be represented in the form: x^2+xy+41y^2 where x and y are integers. For example, g(53)=4 due to (x,y) \\in \\{(-4,1),(-3,-1),(3,1),(4,-1)\\}. diff --git a/src/P805/problem.jl b/src/P805/problem.jl index a294b58..dc12101 100644 --- a/src/P805/problem.jl +++ b/src/P805/problem.jl @@ -3,7 +3,7 @@ module Problem805 title = "Problem 805: Shifted Multiples" published_on = "Saturday, 2nd July 2022, 08:00 pm" -solved_by = 165 +solved_by = 167 difficulty_rating = "55%" content = """ diff --git a/src/P806/problem.jl b/src/P806/problem.jl index 71daab1..2dbf13d 100644 --- a/src/P806/problem.jl +++ b/src/P806/problem.jl @@ -3,7 +3,7 @@ module Problem806 title = "Problem 806: Nim on Towers of Hanoi" published_on = "Saturday, 9th July 2022, 11:00 pm" -solved_by = 101 +solved_by = 104 difficulty_rating = "100%" content = """ This problem combines the game of Nim with the Towers of Hanoi. For a brief introduction to the rules of these games, please diff --git a/src/P807/problem.jl b/src/P807/problem.jl index 14a3431..ef01e18 100644 --- a/src/P807/problem.jl +++ b/src/P807/problem.jl @@ -3,7 +3,7 @@ module Problem807 title = "Problem 807: Loops of Ropes" published_on = "Sunday, 11th September 2022, 02:00 am" -solved_by = 105 +solved_by = 107 difficulty_rating = "90%" content = """ Given a circle C and an integer n > 1, we perform the following operations. diff --git a/src/P808/problem.jl b/src/P808/problem.jl index c572c6f..9b1cfe0 100644 --- a/src/P808/problem.jl +++ b/src/P808/problem.jl @@ -3,7 +3,7 @@ module Problem808 title = "Problem 808: Reversible prime squares" published_on = "Sunday, 18th September 2022, 05:00 am" -solved_by = 1572 +solved_by = 1673 difficulty_rating = "5%" content = """ Both 169 and 961 are the square of a prime. 169 is the reverse of 961. diff --git a/src/P809/problem.jl b/src/P809/problem.jl index 47ceb9f..504432d 100644 --- a/src/P809/problem.jl +++ b/src/P809/problem.jl @@ -3,7 +3,7 @@ module Problem809 title = "Problem 809: Rational Recurrence Relation" published_on = "Sunday, 25th September 2022, 08:00 am" -solved_by = 259 +solved_by = 263 difficulty_rating = "35%" content = """ diff --git a/src/P81/problem.jl b/src/P81/problem.jl index 346ac45..0bb2405 100644 --- a/src/P81/problem.jl +++ b/src/P81/problem.jl @@ -3,7 +3,7 @@ module Problem81 title = "Problem 81: Path sum: two ways" published_on = "Friday, 22nd October 2004, 06:00 pm" -solved_by = 35634 +solved_by = 35718 difficulty_rating = "10%" content = """ In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by \e[1monly moving to the right and down,\e[0m diff --git a/src/P810/problem.jl b/src/P810/problem.jl index 752d5b1..c4724d2 100644 --- a/src/P810/problem.jl +++ b/src/P810/problem.jl @@ -3,7 +3,7 @@ module Problem810 title = "Problem 810: XOR-Primes" published_on = "Sunday, 2nd October 2022, 11:00 am" -solved_by = 547 +solved_by = 573 difficulty_rating = "20%" content = """ We use x ⊕ y for the bitwise XOR of x and y. diff --git a/src/P811/problem.jl b/src/P811/problem.jl index 3d05cd6..ea5fb6c 100644 --- a/src/P811/problem.jl +++ b/src/P811/problem.jl @@ -3,7 +3,7 @@ module Problem811 title = "Problem 811: Bitwise Recursion" published_on = "Saturday, 8th October 2022, 02:00 pm" -solved_by = 198 +solved_by = 204 difficulty_rating = "40%" content = """ Let b(n) be the largest power of 2 that divides n. For example b(24) = 8. diff --git a/src/P812/problem.jl b/src/P812/problem.jl index fef5d25..ec9a9ea 100644 --- a/src/P812/problem.jl +++ b/src/P812/problem.jl @@ -3,7 +3,7 @@ module Problem812 title = "Problem 812: Dynamical Polynomials" published_on = "Saturday, 15th October 2022, 05:00 pm" -solved_by = 90 +solved_by = 97 difficulty_rating = "95%" content = """ A dynamical polynomial is a \e[1;4mmonic\e[0m leading coefficient is 1 polynomial f(x) with integer coefficients such that f(x) divides f(x² - 2). diff --git a/src/P813/problem.jl b/src/P813/problem.jl index 1327ca8..09390c1 100644 --- a/src/P813/problem.jl +++ b/src/P813/problem.jl @@ -3,7 +3,7 @@ module Problem813 title = "Problem 813: XOR-Powers" published_on = "Saturday, 22nd October 2022, 08:00 pm" -solved_by = 405 +solved_by = 431 difficulty_rating = "20%" content = """ We use x\\oplus y to be the bitwise XOR of x and y. diff --git a/src/P814/problem.jl b/src/P814/problem.jl index a33a5cc..be35459 100644 --- a/src/P814/problem.jl +++ b/src/P814/problem.jl @@ -3,7 +3,7 @@ module Problem814 title = "Problem 814: Mezzo-forte" published_on = "Saturday, 29th October 2022, 11:00 pm" -solved_by = 184 +solved_by = 192 difficulty_rating = "50%" content = """ 4n people stand in a circle with their heads down. When the bell rings they all raise their heads and either look at the person diff --git a/src/P815/problem.jl b/src/P815/problem.jl index 69e8583..de71ba5 100644 --- a/src/P815/problem.jl +++ b/src/P815/problem.jl @@ -3,7 +3,7 @@ module Problem815 title = "Problem 815: Group by Value" published_on = "Sunday, 6th November 2022, 01:00 am" -solved_by = 342 +solved_by = 352 difficulty_rating = "25%" content = """ A pack of cards contains 4n cards with four identical cards of each value. The pack is shuffled and cards are dealt one at a diff --git a/src/P816/problem.jl b/src/P816/problem.jl index 984942b..f67b928 100644 --- a/src/P816/problem.jl +++ b/src/P816/problem.jl @@ -3,7 +3,7 @@ module Problem816 title = "Problem 816: Shortest distance among points" published_on = "Sunday, 13th November 2022, 04:00 am" -solved_by = 1128 +solved_by = 1231 difficulty_rating = "5%" content = """ We create an array of points Pₙ in a two dimensional plane using the following random number generator: diff --git a/src/P817/problem.jl b/src/P817/problem.jl index e14af79..f6ce1fd 100644 --- a/src/P817/problem.jl +++ b/src/P817/problem.jl @@ -3,7 +3,7 @@ module Problem817 title = "Problem 817: Digits in Squares" published_on = "Sunday, 20th November 2022, 07:00 am" -solved_by = 355 +solved_by = 372 difficulty_rating = "20%" content = """ diff --git a/src/P818/problem.jl b/src/P818/problem.jl index 040c34b..42a1a20 100644 --- a/src/P818/problem.jl +++ b/src/P818/problem.jl @@ -3,7 +3,7 @@ module Problem818 title = "Problem 818: SET" published_on = "Sunday, 27th November 2022, 10:00 am" -solved_by = 106 +solved_by = 111 difficulty_rating = "85%" content = """ diff --git a/src/P819/problem.jl b/src/P819/problem.jl index 9ec0f8e..986c67b 100644 --- a/src/P819/problem.jl +++ b/src/P819/problem.jl @@ -3,7 +3,7 @@ module Problem819 title = "Problem 819: Iterative Sampling" published_on = "Saturday, 3rd December 2022, 01:00 pm" -solved_by = 182 +solved_by = 190 difficulty_rating = "45%" content = """ Given an n-tuple of numbers another n-tuple is created where each element of the new n-tuple is chosen randomly from the diff --git a/src/P82/problem.jl b/src/P82/problem.jl index 10785f3..edd01da 100644 --- a/src/P82/problem.jl +++ b/src/P82/problem.jl @@ -3,7 +3,7 @@ module Problem82 title = "Problem 82: Path sum: three ways" published_on = "Friday, 5th November 2004, 06:00 pm" -solved_by = 22008 +solved_by = 22073 difficulty_rating = "20%" content = """ NOTE: This problem is a more challenging version of \e[1;35mProblem 81\e[0m. diff --git a/src/P820/problem.jl b/src/P820/problem.jl index 2d74024..cd0eab2 100644 --- a/src/P820/problem.jl +++ b/src/P820/problem.jl @@ -3,7 +3,7 @@ module Problem820 title = "Problem 820: Nth digit of Reciprocals" published_on = "Saturday, 10th December 2022, 04:00 pm" -solved_by = 569 +solved_by = 621 difficulty_rating = "10%" content = """ Let d_n(x) be the n diff --git a/src/P821/problem.jl b/src/P821/problem.jl index 48d222e..29fb5f6 100644 --- a/src/P821/problem.jl +++ b/src/P821/problem.jl @@ -3,7 +3,7 @@ module Problem821 title = "Problem 821: 123-Separable" published_on = "Saturday, 17th December 2022, 07:00 pm" -solved_by = 119 +solved_by = 127 difficulty_rating = "65%" content = """ A set, S, of integers is called 123-separable if S, 2S and 3S are disjoint. Here 2S and 3S are obtained by multiplying all the diff --git a/src/P822/problem.jl b/src/P822/problem.jl index 6752e14..70aad7d 100644 --- a/src/P822/problem.jl +++ b/src/P822/problem.jl @@ -3,7 +3,7 @@ module Problem822 title = "Problem 822: Square the Smallest" published_on = "Saturday, 24th December 2022, 10:00 pm" -solved_by = 508 +solved_by = 555 difficulty_rating = "15%" content = """ diff --git a/src/P823/problem.jl b/src/P823/problem.jl index 2280795..92a6d64 100644 --- a/src/P823/problem.jl +++ b/src/P823/problem.jl @@ -3,7 +3,7 @@ module Problem823 title = "Problem 823: Factor Shuffle" published_on = "Sunday, 1st January 2023, 01:00 am" -solved_by = 155 +solved_by = 162 difficulty_rating = "50%" content = """ A list initially contains the numbers 2, 3, \\dots, n. diff --git a/src/P824/problem.jl b/src/P824/problem.jl index 70ed610..d8abb4d 100644 --- a/src/P824/problem.jl +++ b/src/P824/problem.jl @@ -3,7 +3,7 @@ module Problem824 title = "Problem 824: Chess Sliders" published_on = "Sunday, 8th January 2023, 04:00 am" -solved_by = 82 +solved_by = 85 difficulty_rating = "85%" content = """ A Slider is a chess piece that can move one square left or right. diff --git a/src/P825/problem.jl b/src/P825/problem.jl index 85fe9ea..6366231 100644 --- a/src/P825/problem.jl +++ b/src/P825/problem.jl @@ -3,7 +3,7 @@ module Problem825 title = "Problem 825: Chasing Game" published_on = "Sunday, 15th January 2023, 07:00 am" -solved_by = 119 +solved_by = 127 difficulty_rating = "60%" content = """ Two cars are on a circular track of total length 2n, facing the same direction, initially distance n apart. diff --git a/src/P826/problem.jl b/src/P826/problem.jl index 7ca9568..2af3aa3 100644 --- a/src/P826/problem.jl +++ b/src/P826/problem.jl @@ -3,7 +3,7 @@ module Problem826 title = "Problem 826: Birds on a Wire" published_on = "Sunday, 22nd January 2023, 10:00 am" -solved_by = 185 +solved_by = 195 difficulty_rating = "45%" content = """ Consider a wire of length 1 unit between two posts. Every morning n birds land on it randomly with every point on the wire diff --git a/src/P827/problem.jl b/src/P827/problem.jl index 28bc225..c7e3b82 100644 --- a/src/P827/problem.jl +++ b/src/P827/problem.jl @@ -3,7 +3,7 @@ module Problem827 title = "Problem 827: Pythagorean Triple Occurrence" published_on = "Saturday, 28th January 2023, 01:00 pm" -solved_by = 145 +solved_by = 158 difficulty_rating = "50%" content = """ diff --git a/src/P828/problem.jl b/src/P828/problem.jl index 6ae4db2..4950764 100644 --- a/src/P828/problem.jl +++ b/src/P828/problem.jl @@ -3,7 +3,7 @@ module Problem828 title = "Problem 828: Numbers Challenge" published_on = "Saturday, 4th February 2023, 04:00 pm" -solved_by = 397 +solved_by = 451 difficulty_rating = "15%" content = """ It is a common recreational problem to make a target number using a selection of other numbers. In this problem you will be given six numbers and a target number. diff --git a/src/P829/problem.jl b/src/P829/problem.jl index de91758..dc2eebc 100644 --- a/src/P829/problem.jl +++ b/src/P829/problem.jl @@ -3,7 +3,7 @@ module Problem829 title = "Problem 829: Integral Fusion" published_on = "Saturday, 11th February 2023, 07:00 pm" -solved_by = 173 +solved_by = 182 difficulty_rating = "45%" content = """ Given any integer n>1 a diff --git a/src/P83/problem.jl b/src/P83/problem.jl index cac41b9..9063827 100644 --- a/src/P83/problem.jl +++ b/src/P83/problem.jl @@ -3,7 +3,7 @@ module Problem83 title = "Problem 83: Path sum: four ways" published_on = "Friday, 19th November 2004, 06:00 pm" -solved_by = 18969 +solved_by = 19026 difficulty_rating = "25%" content = """ NOTE: This problem is a more challenging version of \e[1;35mProblem 81\e[0m. diff --git a/src/P830/problem.jl b/src/P830/problem.jl index 07b0e85..027123f 100644 --- a/src/P830/problem.jl +++ b/src/P830/problem.jl @@ -3,7 +3,7 @@ module Problem830 title = "Problem 830: Binomials and Powers" published_on = "Saturday, 18th February 2023, 10:00 pm" -solved_by = 98 +solved_by = 109 difficulty_rating = "75%" content = """ diff --git a/src/P831/problem.jl b/src/P831/problem.jl index 1573230..faa5f8c 100644 --- a/src/P831/problem.jl +++ b/src/P831/problem.jl @@ -3,8 +3,8 @@ module Problem831 title = "Problem 831: Triple Product" published_on = "Sunday, 26th February 2023, 01:00 am" -solved_by = 138 -difficulty_rating = "" +solved_by = 153 +difficulty_rating = "60%" content = """ Let g(m) be the integer defined by the following double sum of products of binomial coefficients: diff --git a/src/P832/problem.jl b/src/P832/problem.jl index 4a4f782..a46879d 100644 --- a/src/P832/problem.jl +++ b/src/P832/problem.jl @@ -3,8 +3,8 @@ module Problem832 title = "Problem 832: Mex Sequence" published_on = "Sunday, 5th March 2023, 04:00 am" -solved_by = 213 -difficulty_rating = "" +solved_by = 234 +difficulty_rating = "30%" content = """ In this problem ⊕ is used to represent the bitwise \e[1mexclusive or\e[0m of two numbers. Starting with blank paper repeatedly do the following: diff --git a/src/P833/problem.jl b/src/P833/problem.jl index ce73857..a5330d7 100644 --- a/src/P833/problem.jl +++ b/src/P833/problem.jl @@ -3,8 +3,8 @@ module Problem833 title = "Problem 833: Square Triangle Products" published_on = "Sunday, 12th March 2023, 07:00 am" -solved_by = 128 -difficulty_rating = "" +solved_by = 142 +difficulty_rating = "65%" content = """ Triangle numbers T_k are integers of the form \\frac{k(k+1)} 2. diff --git a/src/P834/problem.jl b/src/P834/problem.jl index 52a15af..8a04a32 100644 --- a/src/P834/problem.jl +++ b/src/P834/problem.jl @@ -3,8 +3,8 @@ module Problem834 title = "Problem 834: Add and Divide" published_on = "Sunday, 19th March 2023, 10:00 am" -solved_by = 239 -difficulty_rating = "" +solved_by = 280 +difficulty_rating = "25%" content = """ A sequence is created by starting with a positive integer n and incrementing by (n+m) at the m^{th} step. diff --git a/src/P835/problem.jl b/src/P835/problem.jl index 7f1c2ea..f980a75 100644 --- a/src/P835/problem.jl +++ b/src/P835/problem.jl @@ -3,8 +3,8 @@ module Problem835 title = "Problem 835: Supernatural Triangles" published_on = "Saturday, 25th March 2023, 01:00 pm" -solved_by = 231 -difficulty_rating = "" +solved_by = 265 +difficulty_rating = "25%" content = """ A \e[1mPythagorean triangle\e[0m is called supernatural if two of its three sides are consecutive integers. diff --git a/src/P836/problem.jl b/src/P836/problem.jl index 713a060..78bf2bc 100644 --- a/src/P836/problem.jl +++ b/src/P836/problem.jl @@ -3,8 +3,8 @@ module Problem836 title = "Problem 836: A Bold Proposition" published_on = "Saturday, 1st April 2023, 05:00 pm" -solved_by = 765 -difficulty_rating = "" +solved_by = 1021 +difficulty_rating = "5%" content = """ Let A be an \e[1maffine plane\e[0m over a \e[1mradically integral local field\e[0m F with residual characteristic p. diff --git a/src/P837/problem.jl b/src/P837/problem.jl index e2c2854..f1b7cde 100644 --- a/src/P837/problem.jl +++ b/src/P837/problem.jl @@ -3,7 +3,7 @@ module Problem837 title = "Problem 837: Amidakuji" published_on = "Saturday, 1st April 2023, 05:00 pm" -solved_by = 134 +solved_by = 163 difficulty_rating = "" content = """ Amidakuji diff --git a/src/P838/problem.jl b/src/P838/problem.jl index 109a52e..afee140 100644 --- a/src/P838/problem.jl +++ b/src/P838/problem.jl @@ -3,7 +3,7 @@ module Problem838 title = "Problem 838: Not Coprime" published_on = "Saturday, 8th April 2023, 08:00 pm" -solved_by = 311 +solved_by = 389 difficulty_rating = "" content = """ Let f(N) be the smallest positive integer that is not coprime to any positive integer n ≤ N whose least significant digit is 3. diff --git a/src/P839/problem.jl b/src/P839/problem.jl index a34cb83..e2fa67b 100644 --- a/src/P839/problem.jl +++ b/src/P839/problem.jl @@ -3,7 +3,7 @@ module Problem839 title = "Problem 839: Beans in Bowls" published_on = "Saturday, 15th April 2023, 11:00 pm" -solved_by = 212 +solved_by = 270 difficulty_rating = "" content = """ The sequence Sₙ is defined by S₀ = 290797 and Sₙ = Sₙ₋₁² mod 50515093 for n > 0. diff --git a/src/P84/problem.jl b/src/P84/problem.jl index 0a2e436..833e933 100644 --- a/src/P84/problem.jl +++ b/src/P84/problem.jl @@ -3,7 +3,7 @@ module Problem84 title = "Problem 84: Monopoly odds" published_on = "Friday, 3rd December 2004, 06:00 pm" -solved_by = 13263 +solved_by = 13307 difficulty_rating = "35%" content = """ In the game, diff --git a/src/P840/problem.jl b/src/P840/problem.jl index 624610c..95c55ad 100644 --- a/src/P840/problem.jl +++ b/src/P840/problem.jl @@ -3,7 +3,7 @@ module Problem840 title = "Problem 840: Sum of Products" published_on = "Sunday, 23rd April 2023, 02:00 am" -solved_by = 163 +solved_by = 245 difficulty_rating = "" content = """ A diff --git a/src/P841/problem.jl b/src/P841/problem.jl new file mode 100644 index 0000000..01ea47c --- /dev/null +++ b/src/P841/problem.jl @@ -0,0 +1,30 @@ +module Problem841 + + +title = "Problem 841: Regular Star Polygons" +published_on = "Sunday, 30th April 2023, 05:00 am" +solved_by = 141 +difficulty_rating = "" +content = """ +The regular star polygon $\\{p/q\\}$, for coprime integers \$p,q\$ with \$p \\gt 2q \\gt 0\$, is a polygon formed from +\$p\$ edges of equal length and equal internal angles, such that tracing the complete polygon wraps \$q\$ times around +the centre. For example, \${8/3\\}\$ is illustrated below: + +The edges of a regular star polygon intersect one another, dividing the interior into several regions. Define the +alternating shading of a regular star polygon to be a selection of such regions to shade, such that every piece of every +edge has a shaded region on one side and an unshaded region on the other, with the exterior of the polygon unshaded. For +example, the above image shows the alternating shading (in green) of \$\\{8/3\\}\$. + +Let \$A(p, q)\$ be the area of the alternating shading of \$\\{p/q\\}\$, assuming that its inradius is \$1\$. +(The inradius of a regular polygon, star or otherwise, is the distance from its centre to the midpoint of any of its +edges.) For example, in the diagram above, it can be shown that central shaded octagon has area \$8(\\sqrt{2}-1)\$ and +each point's shaded kite has area \$2(\\sqrt{2}-1)\$, giving \$A(8,3) = 24(\\sqrt{2}-1) \\approx 9.9411254970\$. + +You are also given that $A(130021, 50008)\\approx 10.9210371479$, rounded to \$10\$ digits after the decimal point. + +Find \$\\sum_{n=3}^{34} A(F_{n+1},F_{n-1})$, where \$F_j\$ is the Fibonacci sequence with \$F_1=F_2=1\$ +(so \$A(F_{5+1},F_{5-1}) = A(8,3)\$). Give your answer rounded to \$10\$ digits after the decimal point. +""" + + +end # module Problem841 diff --git a/src/P842/problem.jl b/src/P842/problem.jl new file mode 100644 index 0000000..c516c67 --- /dev/null +++ b/src/P842/problem.jl @@ -0,0 +1,27 @@ +module Problem842 + + +title = "Problem 842: Irregular Star Polygons" +published_on = "Sunday, 7th May 2023, 08:00 am" +solved_by = 92 +difficulty_rating = "" +content = """ +Given \$n\$ equally spaced points on a circle, we define an \$n\$-star polygon as an \$n\$-gon having those \$n\$ points +as vertices. Two \$n\$-star polygons differing by a rotation/reflection are considered different. + +For example, there are twelve \$5\$-star polygons shown below. + +For an \$n\$-star polygon \$S\$, let \$I(S)\$ be the number of its self intersection points. +Let \$T(n)\$ be the sum of \$I(S)\$ over all $n$-star polygons \$S\$. +For the example above \$T(5) = 20\$ because in total there are \$20\$ self intersection points. + +Some star polygons may have intersection points made from more than two lines. These are only counted once. For example, +\$S\$, shown below is one of the sixty \$6\$-star polygons. This one has \$I(S) = 4\$. + +You are also given that \$T(8) = 14640\$. + +Find \$\\displaystyle \\sum_{n = 3}^{60}T(n)\$. Give your answer modulo \$(10^9 + 7)\$. +""" + + +end # module Problem842 diff --git a/src/P843/problem.jl b/src/P843/problem.jl new file mode 100644 index 0000000..e40c4a4 --- /dev/null +++ b/src/P843/problem.jl @@ -0,0 +1,24 @@ +module Problem843 + + +title = "Problem 843: Beans in Bowls" +published_on = "Sunday, 14th May 2023, 11:00 am" +solved_by = 76 +difficulty_rating = "" +content = """ +This problem involves an iterative procedure that begins with a circle of n ≥ 3 integers. At each step every number is +simultaneously replaced with the absolute difference of its two neighbours. + +For any initial values, the procedure eventually becomes periodic. + +Let S(N) be the sum of all possible periods for 3 ≤ n ≤ N. For example, S(6) = 6, because the possible periods for +3 ≤ n ≤ 6 are 1, 2, 3. Specifically, n = 3 and n = 4 can each have period 1 only, while n = 5 can have period 1 or 3, and +n = 6 can have period 1 or 2. + +You are also given S(30) = 20381. + +Find S(100). +""" + + +end # module Problem843 diff --git a/src/P844/problem.jl b/src/P844/problem.jl new file mode 100644 index 0000000..3c08266 --- /dev/null +++ b/src/P844/problem.jl @@ -0,0 +1,28 @@ +module Problem844 + + +title = "Problem 844: k-Markov Numbers" +published_on = "Saturday, 20th May 2023, 02:00 pm" +solved_by = 140 +difficulty_rating = "" +content = """ +Consider positive integer solutions to + +\$a^2+b^2+c^2 = 3abc\$ + +For example, \$(1,5,13)\$ is a solution. We define a 3-Markov number to be any part of a solution, so \$1\$, \$5\$ and +\$13\$ are all 3-Markov numbers. Adding distinct 3-Markov numbers \$\\le 10^3\$ would give \$2797\$. + +Now we define a \$k\$-Markov number to be a positive integer that is part of a solution to: + +\$\\displaystyle \\sum_{i=1}^{k}x_i^2=k\\prod_{i=1}^{k}x_i,\\quad x_i\\text{ are positive integers}\$ + +Let \$M_k(N)\$ be the sum of \$k\$-Markov numbers \$\\le N$. Hence \$M_3(10^{3})=2797\$, also \$M_8(10^8) = 131493335\$. + +Define \$\\displaystyle S(K,N)=\\sum_{k=3}^{K}M_k(N)\$. You are given \$S(4, 10^2)=229\$ and \$S(10, 10^8)=2383369980\$. + +Find \$S(10^{18}, 10^{18})\$. Give your answer modulo \$1\\,405\\,695\\,061$. +""" + + +end # module Problem844 diff --git a/src/P845/problem.jl b/src/P845/problem.jl new file mode 100644 index 0000000..9b67d28 --- /dev/null +++ b/src/P845/problem.jl @@ -0,0 +1,16 @@ +module Problem845 + + +title = "Problem 845: Prime Digit Sum" +published_on = "Saturday, 27th May 2023, 05:00 pm" +solved_by = 252 +difficulty_rating = "" +content = """ +Let D(n) be the n-th positive integer that has the sum of its digits a prime. +For example, D(61) = 157 and D(10⁸) = 403539364. + +Find D(10¹⁶). +""" + + +end # module Problem845 diff --git a/src/P846/problem.jl b/src/P846/problem.jl new file mode 100644 index 0000000..5abd92a --- /dev/null +++ b/src/P846/problem.jl @@ -0,0 +1,29 @@ +module Problem846 + + +title = "Problem 846: Magic Bracelets" +published_on = "Saturday, 3rd June 2023, 08:00 pm" +solved_by = 77 +difficulty_rating = "" +content = """ +A bracelet is made by connecting at least three numbered beads in a circle. Each bead can only display \$1\$, \$2\$, or +any number of the form \$p^k\$ or \$2p^k\$ for odd prime \$p\$. + +In addition a magic bracelet must satisfy the following two conditions: + +no two beads display the same number +the product of the numbers of any two adjacent beads is of the form \$x^2+1\$ + +Define the potency of a magic bracelet to be the sum of numbers on its beads. + +The example is a magic bracelet with five beads which has a potency of 155. + +Let \$F(N)\$ be the sum of the potency of each magic bracelet which can be formed using positive integers not exceeding +\$N\$, where rotations and reflections of an arrangement are considered equivalent. You are given \$F(20)=258\$ and +\$F(10^2)=538768\$. + +Find \$F(10^6)\$. +""" + + +end # module Problem846 diff --git a/src/P85/problem.jl b/src/P85/problem.jl index 5a39413..ef3cea5 100644 --- a/src/P85/problem.jl +++ b/src/P85/problem.jl @@ -3,7 +3,7 @@ module Problem85 title = "Problem 85: Counting rectangles" published_on = "Friday, 17th December 2004, 06:00 pm" -solved_by = 25743 +solved_by = 25807 difficulty_rating = "15%" content = """ By counting carefully it can be seen that a rectangular grid measuring 3 by 2 contains eighteen rectangles: diff --git a/src/P86/problem.jl b/src/P86/problem.jl index d53fa52..362e06c 100644 --- a/src/P86/problem.jl +++ b/src/P86/problem.jl @@ -3,7 +3,7 @@ module Problem86 title = "Problem 86: Cuboid route" published_on = "Friday, 7th January 2005, 06:00 pm" -solved_by = 13316 +solved_by = 13349 difficulty_rating = "35%" content = """ A spider, S, sits in one corner of a cuboid room, measuring 6 by 5 by 3, and a fly, F, sits in the opposite corner. By travelling on the surfaces of the room the shortest "straight line" distance from S to F is 10 and the path is shown on the diagram. diff --git a/src/P87/problem.jl b/src/P87/problem.jl index 2dff2a5..29fda87 100644 --- a/src/P87/problem.jl +++ b/src/P87/problem.jl @@ -3,7 +3,7 @@ module Problem87 title = "Problem 87: Prime power triples" published_on = "Friday, 21st January 2005, 06:00 pm" -solved_by = 21774 +solved_by = 21831 difficulty_rating = "20%" content = """ The smallest number expressible as the sum of a prime square, prime cube, and prime fourth power is 28. In fact, there are diff --git a/src/P88/problem.jl b/src/P88/problem.jl index 84e413a..6492396 100644 --- a/src/P88/problem.jl +++ b/src/P88/problem.jl @@ -3,7 +3,7 @@ module Problem88 title = "Problem 88: Product-sum numbers" published_on = "Friday, 4th February 2005, 06:00 pm" -solved_by = 10610 +solved_by = 10650 difficulty_rating = "40%" content = """ A natural number, N, that can be written as the sum and product of a given set of at least two natural numbers, {a₁, a₂, ... , aₖ} diff --git a/src/P89/problem.jl b/src/P89/problem.jl index 9cb719a..b72b4a3 100644 --- a/src/P89/problem.jl +++ b/src/P89/problem.jl @@ -3,7 +3,7 @@ module Problem89 title = "Problem 89: Roman numerals" published_on = "Friday, 18th February 2005, 06:00 pm" -solved_by = 22036 +solved_by = 22083 difficulty_rating = "20%" content = """ For a number written in Roman numerals to be considered valid there are basic rules which must be followed. Even though the diff --git a/src/P9/problem.jl b/src/P9/problem.jl index 402266c..0e3740b 100644 --- a/src/P9/problem.jl +++ b/src/P9/problem.jl @@ -3,7 +3,7 @@ module Problem9 title = "Problem 9: Special Pythagorean triplet" published_on = "Friday, 25th January 2002, 06:00 pm" -solved_by = 364578 +solved_by = 364781 difficulty_rating = "5%" content = """ A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, diff --git a/src/P90/problem.jl b/src/P90/problem.jl index afa2594..763f5d2 100644 --- a/src/P90/problem.jl +++ b/src/P90/problem.jl @@ -3,7 +3,7 @@ module Problem90 title = "Problem 90: Cube digit pairs" published_on = "Friday, 4th March 2005, 06:00 pm" -solved_by = 11833 +solved_by = 11883 difficulty_rating = "40%" content = """ Each of the six faces on a cube has a different digit (0 to 9) written on it; the same is done to a second cube. By placing the two cubes side-by-side in different positions we can form a variety of 2-digit numbers. diff --git a/src/P91/problem.jl b/src/P91/problem.jl index 6313467..068590e 100644 --- a/src/P91/problem.jl +++ b/src/P91/problem.jl @@ -3,7 +3,7 @@ module Problem91 title = "Problem 91: Right triangles with integer coordinates" published_on = "Friday, 18th March 2005, 06:00 pm" -solved_by = 16124 +solved_by = 16169 difficulty_rating = "25%" content = """ The points P ( diff --git a/src/P92/problem.jl b/src/P92/problem.jl index 39fef2d..4c87fc3 100644 --- a/src/P92/problem.jl +++ b/src/P92/problem.jl @@ -3,7 +3,7 @@ module Problem92 title = "Problem 92: Square digit chains" published_on = "Friday, 1st April 2005, 06:00 pm" -solved_by = 43086 +solved_by = 43174 difficulty_rating = "5%" content = """ A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before. diff --git a/src/P93/problem.jl b/src/P93/problem.jl index 8fb1852..c8b79c7 100644 --- a/src/P93/problem.jl +++ b/src/P93/problem.jl @@ -3,7 +3,7 @@ module Problem93 title = "Problem 93: Arithmetic expressions" published_on = "Friday, 15th April 2005, 06:00 pm" -solved_by = 12380 +solved_by = 12421 difficulty_rating = "35%" content = """ By using each of the digits from the set, {1, 2, 3, 4}, exactly once, and making use of the four arithmetic operations (+, -, *, /) diff --git a/src/P94/problem.jl b/src/P94/problem.jl index 332a63b..de140f1 100644 --- a/src/P94/problem.jl +++ b/src/P94/problem.jl @@ -3,7 +3,7 @@ module Problem94 title = "Problem 94: Almost equilateral triangles" published_on = "Friday, 29th April 2005, 06:00 pm" -solved_by = 12970 +solved_by = 13010 difficulty_rating = "35%" content = """ It is easily proved that no equilateral triangle exists with integral length sides and integral area. However, the almost equilateral diff --git a/src/P95/problem.jl b/src/P95/problem.jl index 7ffec60..17d6089 100644 --- a/src/P95/problem.jl +++ b/src/P95/problem.jl @@ -3,7 +3,7 @@ module Problem95 title = "Problem 95: Amicable chains" published_on = "Friday, 13th May 2005, 06:00 pm" -solved_by = 14994 +solved_by = 15043 difficulty_rating = "30%" content = """ The proper divisors of a number are all the divisors excluding the number itself. For example, the proper divisors of 28 are 1, 2, diff --git a/src/P96/problem.jl b/src/P96/problem.jl index d408af7..c159398 100644 --- a/src/P96/problem.jl +++ b/src/P96/problem.jl @@ -3,7 +3,7 @@ module Problem96 title = "Problem 96: Su Doku" published_on = "Friday, 27th May 2005, 06:00 pm" -solved_by = 17936 +solved_by = 17987 difficulty_rating = "25%" content = """ Su Doku (Japanese meaning number place) is the name given to a popular puzzle concept. Its origin is unclear, but credit must diff --git a/src/P97/problem.jl b/src/P97/problem.jl index a735287..981c20a 100644 --- a/src/P97/problem.jl +++ b/src/P97/problem.jl @@ -3,7 +3,7 @@ module Problem97 title = "Problem 97: Large non-Mersenne prime" published_on = "Friday, 10th June 2005, 06:00 pm" -solved_by = 44647 +solved_by = 44732 difficulty_rating = "5%" content = """ The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form diff --git a/src/P98/problem.jl b/src/P98/problem.jl index 177abe2..bd5d36d 100644 --- a/src/P98/problem.jl +++ b/src/P98/problem.jl @@ -3,7 +3,7 @@ module Problem98 title = "Problem 98: Anagramic squares" published_on = "Friday, 17th June 2005, 06:00 pm" -solved_by = 11959 +solved_by = 11990 difficulty_rating = "35%" content = """ By replacing each of the letters in the word CARE with 1, 2, 9, and 6 respectively, we form a square number: 1296 = 36². What diff --git a/src/P99/problem.jl b/src/P99/problem.jl index 9786813..6e93331 100644 --- a/src/P99/problem.jl +++ b/src/P99/problem.jl @@ -3,7 +3,7 @@ module Problem99 title = "Problem 99: Largest exponential" published_on = "Friday, 1st July 2005, 06:00 pm" -solved_by = 31748 +solved_by = 31811 difficulty_rating = "10%" content = """ Comparing two numbers written in index form like 2¹¹ and 3⁷ is not difficult, as any calculator would confirm that 2¹¹ = 2048 < diff --git a/src/problemfiles.jl b/src/problemfiles.jl index 3260c03..e5ff50c 100644 --- a/src/problemfiles.jl +++ b/src/problemfiles.jl @@ -838,3 +838,9 @@ include("P836/problem.jl") include("P838/problem.jl") include("P839/problem.jl") #include("P840/problem.jl") +#include("P841/problem.jl") +#include("P842/problem.jl") +include("P843/problem.jl") +#include("P844/problem.jl") +include("P845/problem.jl") +#include("P846/problem.jl") diff --git a/src/unedited_questions.txt b/src/unedited_questions.txt index 1041983..f4c32bb 100644 --- a/src/unedited_questions.txt +++ b/src/unedited_questions.txt @@ -141,6 +141,9 @@ Problem 781 Problem 786 Problem 807 Problem 837 +Problem 841 +Problem 842 +Problem 846 #======================================================================================================# # Due to the REPL's inability to render complex mathematical equations, these problems were not edited # # @@ -319,3 +322,4 @@ Problem 833 Problem 834 Problem 835 Problem 840 +Problem 844