# Project Euler #9: Special Pythogorean triplet

This article is part of a series where I'll be diving head first into the Project Euler puzzles. I want to document the challenge of solving such a puzzle and how I got to the answer. I want to prefix this by stating that I can't cheat for any of these challenges; with that I mean I can't look up any other implementations online. After the implementation, I will validate the answer by using this document or a similar sheet.

``````fn is_triplet(x: i32, y: i32, z: i32) -> bool {
if y < x || z < y {
return false
}

let powers = (x.pow(2) + y.pow(2)) as f32;
let result = powers.sqrt();

result == z as f32
}

fn find_triplet(total: i32) -> (i32, i32, i32) {
let (mut x, mut y, mut z) = (1, 2, total - 3);

'x: loop {
while (z - y) > 1 {
z -= 1;
y += 1;

if is_triplet(x, y, z) {
break 'x;
}
}
x += 1;
y = x + 1;
z = total - x - y;

if is_triplet(x, y, z) {
break;
}
}

(x, y, z)
}

#[test]
fn pythagorean_triplet() {
assert_eq!(is_triplet(3,4,5), true);
assert_eq!(is_triplet(3,4,6), false);
assert_eq!(is_triplet(6,8,10), true);
assert_eq!(is_triplet(48,55,73), true);
assert_eq!(is_triplet(17,144,145), true);
}

#[test]
fn find_triplet_test() {
assert_eq!(find_triplet(12), (3, 4, 5));
assert_eq!(find_triplet(24), (6, 8, 10));
assert_eq!(find_triplet(176), (48, 55, 73));
assert_eq!(find_triplet(1000), (200, 375, 425));
}
``````

The full solution is available on GitHub.