Project Euler
GithubProject Euler is a website dedicated to challenging those interested in mathematics by posing increasingly difficult math problems that require "more than just mathematical insights" to solve. While these problems can be solved using any means possible, a knowledge of computer programming (of any language) is required for the vast majority of problems. All of my solutions are done using C++. My solutions for the first 100 problems can be found on Github and a selected few are posted here. For more information about the project check out their about page, or to see the list of problems check out their archives.
If you already have an account on Project Euler, feel free to add me!
Selected Problems
Problem 63
Powerful digit counts
The 5-digit number 16,807 is also a fifth power (16,807 = 75). How many n-digit positive integers exist which are also an nth power?
ViewProblem 64
Odd period square roots
All square roots can be written as periodic continued fractions. How many positive integer square roots ≤ 10,000 have an odd period?
ViewProblem 75
Singular integer right triangles
It turns out that 12cm is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way (3cm, 4cm, 5cm). For every wire length up to 1,500,000cm, how many can form exactly one integer sided right angle triangle?
ViewProblem 76
Counting summations
It is possible to write 5 as a sum in exactly 6 different ways (4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1). How many different ways can 100 be written as a sum of at least 2 positive integers?
ViewProblem 83
Path sum: four ways
Given a matrix of positive integer values, find its minimal path sum from top left to bottom right where the path can be created by moving either left, right, up, or down.
ViewProblem 89
Roman numerals
Valid Roman numerals must follow several basic rules. However, some numbers may be validly written in more than one way. The "best" way of writing a number is the one using the least number of numerals. Given a list of 1,000 Roman numerals, find the number of characters saved by writing each in their minimal form.
ViewProblem 91
Right triangles with integer coordinates
Given a coordinate grid of size 2x2, you can plot 14 triangles containing a right angle that contain 1 point at the origin and the other 2 points at integer coordinates. How many right angle triangles can you plot on a 50x50 grid?
ViewProblem 93
Arithmetic expressions
By using the four numbers {1, 2, 3, 4}, the basic arithmetic operations (+, −, ×, ÷), and brackets, you can create arithmetic expressions that reach every target number from 1 to 28 before hitting an unreachable target (29). Which 4 distinct digits < 10 produce the longest consecutive set of target numbers?
ViewProblem 95
Amicable chains
An Aliquot sum is the sum of a number's proper divisors. An amicable chain is a chain of numbers where each number's aliquot sum points to the next number in the chain. Find the longest amicable chain of numbers without exceeding 1,000,000.
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