Problem #58 is another example of a Project Euler problem where the process of Engineer’s Induction can be very useful. The question reads: Project Euler Problem 58: Spiral primes Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. 37 36 35 34 33 32 31 38 17 16 15 …
Tag Archives: Coding
Project Euler Problem #57
Problem #57 is the first of several Project Euler problems to involve infinite continued fractions for irrational numbers, and it is the first of several problems that can b killed with Pell Equations. The problem reads: Project Euler Problem 57: Square root convergents It is possible to show that the square root of two can …
Project Euler Problem #56
Problem #56 concerns the sum of the digits of various perfect powers. The question reads: Project Euler Problem 56: Powerful digit sum A googol (10100) is a massive number: one followed by one-hundred zeros; 100100 is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is …
Project Euler Problem #55
Problem #55 involves an obscure type of number called a Lychrel number. The question reads: Project Euler Problem 55: Lychrel numbers If we take 47, reverse and add, 47 + 74 = 121, which is palindromic. Not all numbers produce palindromes so quickly. For example, 349 + 943 = 1292, 1292 + 2921 = 4213 …
Project Euler Problem #53
Problem #53 is one of the many problems in Project Euler that involves binomial coefficients. The question reads: Project Euler Problem 53: Combinatoric selections There are exactly ten ways of selecting three from five, 12345: 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345 In combinatorics, we use the notation, (5 choose 3)=10. …
Project Euler Problem #52
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 …
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 …
The Inner Machinations of Walker 