Project Euler – Problem 45 Solution

Yan Cui

I help clients go faster for less using serverless technologies.

Problem

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

image

It can be verified that T285 = P165 = H143 = 40755.

Find the next triangle number that is also pentagonal and hexagonal.

Solution

let naturalNumbers n = Seq.unfold (fun state -> Some(state, state + 1I)) n

// define the function T, P and H
let T n = n * (n + 1I) / 2I
let P n = n * (3I * n - 1I) / 2I
let H n = n * (2I * n - 1I)

// define the sequences for each function from the point the brief left off at
let TSeq = naturalNumbers 285I |> Seq.map T
let PSeq = naturalNumbers 165I |> Seq.map P
let HSeq = naturalNumbers 143I |> Seq.map H

let answer =
    HSeq
    |> Seq.skip 1
    |> Seq.filter (fun h -> PSeq |> Seq.takeWhile (fun p -> p <= h) |> Seq.exists (fun p -> p = h))
    |> Seq.filter (fun h -> TSeq |> Seq.takeWhile (fun t -> t <= h) |> Seq.exists (fun t -> t = h))
    |> Seq.head

Whenever you’re ready, here are 3 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. 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.
  3. 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Your email address will not be published.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 *