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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...

Project Euler 22: Names scores – SOLVED

Project Euler 22 Problem Statement Project Euler 22: Using names.txt, a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical...

Project Euler 23: Non-abundant sums – SOLVED

Project Euler 23 Problem Statement 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 the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number. A...

Project Euler 24: Lexicographic permutations – SOLVED

Project Euler 24 Problem Statement A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The...

Project Euler 25: N-digit Fibonacci number – SOLVED

Project Euler 25 Problem Statement The Fibonacci sequence is defined by the recurrence relation: Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be: {1,1,2,3,5,8,13,21,34,55,89,144} The 12th term, F12, is the first term to contain three...

Project Euler 26: Reciprocal cycles – SOLVED

Project Euler 26 Problem Statement A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given: 1/2= 0.5 1/3= 0.(3) 1/4= 0.25 1/5= 0.2 1/6= 0.1(6) 1/7= 0.(142857)...

Project Euler 27: Quadratic primes – SOLVED

Project Euler 27 Problem Statement Project Euler 27: Euler published the remarkable quadratic formula: n² + n + 41 It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41...

Project Euler 28: Number spiral diagonals – SOLVED

Project Euler 28 Problem Statement Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: 21 22 23 24 25 20 7 8 9 10 19 6 1 2 11 18 5 4 3 12 17 16 15 14 13 It can be verified that the sum of both diagonals is...

Project Euler 29: Distinct powers – SOLVED

Project Euler 29 Problem Statement Originally published on blog.dreamshire.com, M. Molony, APRIL 7, 2009. Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5: 22=4, 23=8, 24=16, 25=32 32=9, 33=27, 34=81, 35=243 42=16, 43=64, 44=256, 45=1024...

Project Euler 30: Digit nth powers – SOLVED

Project Euler 30 Problem Statement Originally published on blog.dreamshire.com, M. Molony, MARCH 30, 2009. Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474...