curiousnumber.fs

module CuriousNumbers

open FsUnit
open Xunit

let rec digits = function
    | 0 -> []
    | x ->
        let remainder = x % 10
        let next = digits (x / 10)   
        remainder :: next

let rec factorial = function
    | 1 | 0 -> 1
    | x -> x * factorial (x - 1)

let factorialLookup = [for i in 0..9 -> factorial i ]

let sum =
    let calc x =
        digits x |> List.map (fun x -> factorialLookup.[x]) |> List.sum
    let isCurious x =
        x = calc x
    [ 10..40730 ] |> List.filter isCurious |> List.sum
 

[<Fact>]
let ``123 breaks into [1;2;3]``() =
    digits 123 |> should equal [3;2;1]

[<Fact>]
let ``factorial of 4 is 24``() =
    factorial 4 |> should equal 24

[<Fact>]
let ``factorial lookup of 4 is 24``() =
    factorialLookup.[4] |> should equal 24

[<Fact>]
let ``sum of curious numbers should be 40730``() =
    sum |> should equal 40730