### Integer Right Triangles (Project Euler Problem 39)

**Poblem**If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p ≤ 1000, is the number of solutions maximised?

Link to original problem description

**Solution**```
open System
let buildArrays xs ys zs limits = seq{
for x in xs do
for y in ys do
if x < y then
for z in zs do
if (x*x + y*y = z*z) then
for limit in limits do
if (x + y + z = limit) then
yield limit, x, y, z}
let First (a,b,c,d) = a
let pyhtosArrays = buildArrays [1..999] [1..999] [1..999] [1..999]
|> Seq.toList
|> List.map (fun x -> First x)
let results = pyhtosArrays |> Seq.countBy id
|> Seq.toList
|> List.sortByDescending snd
```