# Project Euler – Problem 62 Solution

#### 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)

// 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)

// find the smallest elements in the groups
groups |> Seq.map (fun (k, l) -> l |> Seq.min) |> Seq.min
```

### 2 thoughts on “Project Euler – Problem 62 Solution”

1. Your use of groupBy to find the permutations is *extremely* clever.

2. thank you :-)