Project Euler 12: Highly divisible triangular number

Project Euler 12 Problem Statement Project Euler 12: The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...

Project Euler 14: Longest Collatz sequence

Project Euler 14 Problem Statement Originally published on blog.dreamshire.com, M. Molony, MAY 18, 2009. The following iterative sequence is defined for the set of positive integers: n → n/2 (n is even) n → 3n + 1 (n is odd) Using the rule above and starting...

Project Euler 17: Numbers to words

Project Euler 17 Problem Statement 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 total. If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many...

Project Euler 18: Maximum path sum I

Project Euler 18 Problem Statement Originally published on blog.dreamshire.com, M. Molony, APRIL 1, 2009. By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 5 2 4 6 8 5 9 3 That...

Project Euler 21: Amicable numbers

Project Euler 21 Problem Statement Project Euler 21: Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called...