# Project Euler: Problem 9

A Pythagorean triplet is a set of three natural numbers, for which, For example, There exists exactly one Pythagorean triplet for which, Find the product abc.

## Solution

This I wasn’t quite sure how to solve effectively and my solution is probably not the fastest or most clever, but at least it is pretty simple 🙂 To start off, we need a source of Pythagorean triplets.

public class PythagoreanTriples
: IEnumerable<Triple<ulong, ulong, ulong>>
{
public IEnumerator<Triple<ulong, ulong, ulong>> GetEnumerator()
{
for (ulong c = 1;; c++)
for (ulong b = 1; b <= c; b++)
for (ulong a = 1; a < b; a++)
if ((a*a) + (b*b) == c*c)
yield return Tuple.From(a, b, c);
}

IEnumerator IEnumerable.GetEnumerator()
{
return GetEnumerator();
}
}

You can find the Triple class in a library called the Lokad Shared Libraries.

Anyways, that’s pretty much what we need to solve this problem actually. We can use it like so:

var t = new PythagoreanTriples()
.First(x => x.Item1 + x.Item2 + x.Item3 == 1000);
var answer = t.Item1 * t.Item2 * t.Item3;

This piece of code simply goes through triplets until it finds the first one fulfilling our requirement. It runs in around 230 milliseconds, which is acceptable enough.