Yan Cui
I help clients go faster for less using serverless technologies.
This article is brought to you by
The real-time data platform that empowers developers to build innovative products faster and more reliably than ever before.
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
Whenever you’re ready, here are 4 ways I can help you:
- Production-Ready Serverless: Join 20+ AWS Heroes & Community Builders and 1000+ other students in levelling up your serverless game. This is your one-stop shop for quickly levelling up your serverless skills.
- Do you want to know how to test serverless architectures with a fast dev & test loop? Check out my latest course, Testing Serverless Architectures and learn the smart way to test serverless.
- I help clients launch product ideas, improve their development processes and upskill their teams. If you’d like to work together, then let’s get in touch.
- Join my community on Discord, ask questions, and join the discussion on all things AWS and Serverless.
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.