Merge pull request #10 from udohjeremiah/newproblems

update old problems and add new ones
udohjeremiah · Jun 5, 2023 · f45e6e3 · f45e6e3
2 parents 75686d2 + 685638d
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diff --git 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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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
@@ -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.