Project Euler – Problem 62 Solution

You can become a serverless blackbelt. Enrol to my 4-week online workshop Production-Ready Serverless and gain hands-on experience building something from scratch using serverless technologies. At the end of the workshop, you should have a broader view of the challenges you will face as your serverless architecture matures and expands. You should also have a firm grasp on when serverless is a good fit for your system as well as common pitfalls you need to avoid. Sign up now and get 15% discount with the code yanprs15!

Problem

The cube, 41063625 (3453), can be permuted to produce two other cubes: 56623104 (3843) and 66430125 (4053). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.

Find the smallest cube for which exactly five permutations of its digits are cube.

Solution

open System

let cubeRoot (n:int64) = Math.Pow(double(n), 1.0/3.0)

// define function to investigate the numbers of d digits which are cubes
let f d =
    // find the min & max number whose cube is d digits long
    let min, max = int64(cubeRoot (pown 10L d)), int64(cubeRoot (pown 10L (d+1)))

    // and look for groups of 5 numbers which are cubes and permutations of one another
    [min..max]
    |> List.map (fun n -> pown n 3)
    |> Seq.groupBy (fun n -> n.ToString().ToCharArray() |> Array.sort)
    |> Seq.filter (fun (k, l) -> l |> Seq.length = 5)

let answer =
    // go through the numbers of a given number of digits and find the first set of groups
    // of 5 numbers which are cubes and permutations of one another
    let groups =
        Seq.unfold (fun state -> Some(state, state+1)) 7
        |> Seq.map f
        |> Seq.filter (fun l -> Seq.length l > 0)
        |> Seq.head

    // find the smallest elements in the groups
    groups |> Seq.map (fun (k, l) -> l |> Seq.min) |> Seq.min
Liked this article? Support me on Patreon and get direct help from me via a private Slack channel or 1-2-1 mentoring.
Subscribe to my weekly newsletter


Hi, I’m Yan. I’m an AWS Serverless Hero and I help companies go faster for less by adopting serverless technologies successfully.

Are you struggling with serverless or need guidance on best practices? Do you want someone to review your architecture and help you avoid costly mistakes down the line? Whatever the case, I’m here to help.

Hire me.


Skill up your serverless game with this hands-on workshop.

My 4-week Production-Ready Serverless online workshop is back!

This course takes you through building a production-ready serverless web application from testing, deployment, security, all the way through to observability. The motivation for this course is to give you hands-on experience building something with serverless technologies while giving you a broader view of the challenges you will face as the architecture matures and expands.

We will start at the basics and give you a firm introduction to Lambda and all the relevant concepts and service features (including the latest announcements in 2020). And then gradually ramping up and cover a wide array of topics such as API security, testing strategies, CI/CD, secret management, and operational best practices for monitoring and troubleshooting.

If you enrol now you can also get 15% OFF with the promo code “yanprs15”.

Enrol now and SAVE 15%.


Check out my new podcast Real-World Serverless where I talk with engineers who are building amazing things with serverless technologies and discuss the real-world use cases and challenges they face. If you’re interested in what people are actually doing with serverless and what it’s really like to be working with serverless day-to-day, then this is the podcast for you.


Check out my new course, Learn you some Lambda best practice for great good! In this course, you will learn best practices for working with AWS Lambda in terms of performance, cost, security, scalability, resilience and observability. We will also cover latest features from re:Invent 2019 such as Provisioned Concurrency and Lambda Destinations. Enrol now and start learning!


Check out my video course, Complete Guide to AWS Step Functions. In this course, we’ll cover everything you need to know to use AWS Step Functions service effectively. There is something for everyone from beginners to more advanced users looking for design patterns and best practices. Enrol now and start learning!