➰ Project Euler

Largest product in a series

A testbed for playing with the scenario of Project Euler 208

All Project Euler problems, and my solutions to some of them

Find the number of ways to make n pence using any number of coins

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital, where n is the number of digits.

Find the sum of all numbers which are equal to the sum of the factorial of their digits. Note: As 1! = 1 and 2! = 2 are not sums, they are not included.

The decimal number 585 = 1001001001 (Base 2) is palindromic in both bases. The aim is to find the sum of all numbers less than n, whereas n is between 1000 and 1000000, which are palindromic in base 10 and base 2. (Please note that the palindromic number, in either base, may not include leading zeros.)

Find the largest 1 to k pandigital k-digit number that can be formed as the concatenated product of an integer (1,2,...,n) where n is greater than 1.

Find the perimeter less than or equal to n (e.g. 1000), for which the number of solutions is maximised.

Find the number of triangle words in the provided array. A PDF File is available for viewing the words. A triangle word is whose word value is a triangle number. A word value is the sum of numbers corresponding to its alphabetical position. For example, SKY has a word value of 55, because 19 + 11 + 25 = 55. SKY is a triangle word, because 55 is …

The aim is to find the sum of 0 to n pandigital numbers with sub-strings fulfilling n-2 of the properties (Divisible by 2, 3, 5, 7, 11, 13 and 17).

Pentagonal Numbers are generated by the formula Pn = n(3n-1)/2. The first ten pentagonal numbers are 1, 5, 12, 22, 35, 51, 70, 92, 117, 145. The aim is to find the pair of pentagonal numbers, Pj and Pk , for which their sum and difference is pentagonal and D = |Pk - Pj| is minimised. Find the value of D.

Triangle Numbers are generated by the formula Tn = n(n+1)/2 - Its numbers are 1, 3, 6, 10, 15,.... Pentagonal Numbers are generated by the formula Pn = n(3n-1)/2 - Its numbers are 1, 5, 12, 22, 35,.... Hexagonal numbers are generated by the formula Hn = n(2n-1) - Its numbers are 1, 6, 15, 28, 45,.... It can be verified that T285 = P165 = H143 = …

Find the smallest odd composite that cannot be written as the sum of a prime and twice a square as described in https://projecteuler.net/problem=46

Finds the first consecutive number in the consecutive numbers to have a certain number of distinct prime factors each. For example, 14 is the first consecutive number of two consecutive numbers (14 and 15) to have two distinct prime factors.

Find the smallest positive integer, such that multiplied by integers 2, 3, ..., n contain the same digits.

Find the number of values of nCr for 1 ≤ n ≤ 100, greater than one-million or other limits.

Counts the number of Lychrel Numbers below the limit (e.g. 10000)