Problem #52 is one of the few problems on Project Euler where many people will already know the answer before solving the question. The question reads: Project Euler Problem 52: Permuted multiples It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order. Find …
Category Archives: Project Euler Problems
Project Euler Problem #51
Problem #51 is one of the many problems that involves manipulating digits in prime numbers. The question reads: Project Euler Problem 51: Prime digit replacements 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 all prime. By …
Project Euler Problem #50
Problem #50 involves sums of consecutive primes. The question reads: Project Euler Problem 50: Consecutive prime sum The prime 41, can be written as the sum of six consecutive primes: 41 = 2 + 3 + 5 + 7 + 11 + 13 This is the longest sum of consecutive primes that adds to a …
Project Euler Problem #49
Problem #49 involves arithmetic sequences where the elements of the sequences are rearrangements of the digits in the other terms of the sequence. The problem reads: Project Euler Problem 49: Prime permutations The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of …
Project Euler Problem #48
Problem #48 is one of the many problems on Project Euler that involves modular arithmetic. The question reads: Project Euler Problem 48: Self powers The series, 11 + 22 + 33 + … + 1010 = 10405071317. Find the last ten digits of the series, 11 + 22 + 33 + … + 10001000. My solution involves a common technique for finding …
Project Euler Problem #47
Problem #47 is one of the many Project Euler problems that involves prime numbers. The problem reads: Project Euler Problem 47: Distinct primes factors The first two consecutive numbers to have two distinct prime factors are: 14 = 2 × 7 15 = 3 × 5 The first three consecutive numbers to have three distinct …
Project Euler Problem #46
Problem #46 involves a disproved conjecture by the famous mathematician Christian Goldbach. The problem reads: Project Euler Problem 46: Goldbach’s other conjecture It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. 9 = 7 + 2×12 15 = 7 + …
Project Euler Problem #45
Problem #45 is yet another problem that involves figurate numbers. The problem reads: Project Euler Problem 45: Triangular, pentagonal, and hexagonal Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: Triangle Tn=n(n+1)/2 1, 3, 6, 10, 15, … Pentagonal Pn=n(3n−1)/2 1, 5, 12, 22, 35, … Hexagonal Hn=n(2n−1) 1, 6, 15, 28, 45, …
Project Euler Problem #44:
Problem #44 concerns a somewhat obscure class of numbers known as the pentagonal numbers. It is also (in my opinion) the most difficult question in the first 50 problems of Project Euler, and the only one that I have yet to find a solution for that runs in under a minute. (I’m a very sloppy …
Project Euler Problem #43
Problem #43 is yet another problem that involves digits and primes. This time, we’re looking at pandigital numbers where each subsequence is divisible by a different prime. Here’s the problem: Project Euler Problem 43: Sub-string divisibility The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the …
The Inner Machinations of Walker 