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 …
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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 …
Project Euler Problem #42
Problem #42 is yet another simple question that involves analyzing a file with tons of data. The question reads: Project Euler Problem 42: Coded triangle numbers The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, … …
Project Euler Problem #41:
Problem #41 is yet another problem that involves digits in the prime numbers. The question reads: Project Euler Problem 41: Pandigital prime We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime. What is the …
Project Euler Problem #40:
Problem #40 involves an obscure constant in mathematics known as the Champernowne constant. This constant is relevant because it is one of the few numbers that has been proven to be transcendental. The problem reads: Project Euler Problem 40: Champernowne’s constant An irrational decimal fraction is created by concatenating the positive integers: 0.123456789101112131415161718192021… It can …
Project Euler Problem #39:
Problem #39 is one of the many problems on Project Euler that involves Pythagorean Triples. In fact, this type of problem is so common that my solution to this problem is nearly identical to my solution for Problem #9. The question reads: Project Euler Problem 39: Integer right triangles If p is the perimeter of a right …
Project Euler Problem #38:
Problem #38 is one of the many problems on Project Euler that requires permutations of the digits 1-9, also known as pandigitals. The question reads: Project Euler Problem 38: Pandigital multiples Take the number 192 and multiply it by each of 1, 2, and 3: 192 × 1 = 192 192 × 2 = 384 …
The Inner Machinations of Walker 