#### Problem

*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?*

#### Solution

// define function to find the number of solutions for p
let countSolutions p =
[4*p/10..6*p/10]
|> List.filter (fun c ->
[1..p]
|> Seq.takeWhile (fun b -> b + c < p)
|> Seq.exists (fun b -> (pown (p-b-c) 2 + pown b 2) = pown c 2))
|> List.length
let answer = [1..1000] |> List.maxBy countSolutions

I have to remind myself that sometimes it’s better to work backwards. As usual, your solution is better than mine :) You started with possible Cs and generated possible As and Bs from that, whereas I started with As and Bs, computed C, and filtered any combination thereof that didn’t look “right” (get it? it’s a triangle joke! I kill me).

At one point, I must have known that the hypotenuse is between 0.4p and 0.6p, but apparently I’ve forgotten that in the 30 years since I learned it.