Project Euler – Problem 53 Solution

Yan Cui

I help clients go faster for less using serverless technologies.

This article is brought to you by

Is your CI build step taking too long? Try Depot for free today and experience up to 40x faster build speed!

Unlock faster CI for FREE

Problem

There are exactly ten ways of selecting three from five, 12345:

123, 124, 125, 134, 135, 145, 234, 235, 245, and 345

In combinatorics, we use the notation, 5C3 = 10.

In general,

image

It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.

How many, not necessarily distinct, values of  nCr, for 1 <= n <= 100, are greater than one-million?

Solution

let factorial n = if (n = 0I) then 1I else [1I..n] |> List.reduce (*)

let C n r = if r <= n then (factorial n) / ((factorial r) * (factorial (n - r))) else 0I

let answer =
    &#91;1I..100I&#93;
    |> List.collect (fun n -> [1I..n] |> List.map (fun r -> C n r))
    |> List.filter (fun x -> x > 1000000I)
    |> List.length

Whenever you’re ready, here are 4 ways I can help you:

  1. 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.
  2. 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.
  3. 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.
  4. Join my community on Discord, ask questions, and join the discussion on all things AWS and Serverless.

Leave a Comment

Your email address will not be published. Required fields are marked *