Project Euler – Problem 28 Solution

Yan Cui

I help clients go faster for less using serverless technologies.


Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:


It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?


let rec sumDiagonals n m total max =
    match n with
    | 1 -> sumDiagonals (n+1) m 1 1
    | _ when n > m -> total
    | _ when n % 2 = 0 -> sumDiagonals (n+1) m total max
    | _ ->
        let newValues = [1..4] |> (fun x -> max + x * (n-1))
        let newMax = newValues |> List.max
        let newTotal = total + (newValues |> List.sum)
        sumDiagonals (n+1) m newTotal newMax

let answer = sumDiagonals 1 1001 0 0

As you’ve probably noticed already, there’s a pattern in the sequence 1, 3, 5, 7, 9, 13, 17, 21, 25, … generated by the spiral in the problem brief. As the dimension goes up by 2 at a time, all odd numbers, 4 new numbers are added to the sequence:

Dimension (d) Numbers on the edge of the square Max number from last dimension
1 1
3 3, 5, 7, 9 1
5 13, 17, 21, 25 9

Looking at the above table, it quickly becomes clear that the new numbers that are added to the diagonals when you expand the dimension by 2 can be calculated as:

max number from last dimension + (d-1) * i (where i is a number from 1 to 4)

My solution simply wraps this logic in a recursive function whilst keeping a running total of all the numbers that have been generated.


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

  1. If you want a one-stop shop to help you quickly level up your serverless skills, you should check out my Production-Ready Serverless workshop. Over 20 AWS Heroes & Community Builders have passed through this workshop, plus 1000+ students from the likes of AWS, LEGO, Booking, HBO and Siemens.
  2. If you want to learn how to test serverless applications without all the pain and hassle, you should check out my latest course, Testing Serverless Architectures.
  3. If you’re a manager or founder and want to help your team move faster and build better software, then check out my consulting services.
  4. If you just want to hang out, talk serverless, or ask for help, then you should join my FREE Community.


Leave a Comment

Your email address will not be published.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