Project Euler – Problem 39 Solution

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


Yan Cui

I’m an AWS Serverless Hero and the author of Production-Ready Serverless. I have run production workload at scale in AWS for nearly 10 years and I have been an architect or principal engineer with a variety of industries ranging from banking, e-commerce, sports streaming to mobile gaming. I currently work as an independent consultant focused on AWS and serverless.

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