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 ðŸ™‚ To start off, we need a source of Pythagorean triplets.

: 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:

.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.

Do you have a more clever way to do this? Please leave a comment and share ðŸ™‚