Yan Cui

I help clients go faster for less using serverless technologies.

#### Problem

The cube, 41063625 (345^{3}), can be permuted to produce two other cubes: 56623104 (384^{3}) and 66430125 (405^{3}). 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

**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.

Bryan SlatnerYour use of groupBy to find the permutations is *extremely* clever.

Yan Cuithank you :-)