# Project Euler – Problem 34 Solution

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#### Problem

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: as 1! = 1 and 2! = 2 are not sums they are not included.

#### Solution

```open System.Collections.Generic

// factorial function
let factorial n = if (n = 0) then 1 else [1..n] |> List.reduce (fun acc x -> acc * x)

// create a cache of sorts to help improve performance
let factorials = new Dictionary<int, int>()

let start = [0..9] |> List.iter (fun n -> factorials.Add(n, (factorial n)))

// get the digits of a number into an array
let getDigits (n:bigint) =
n.ToString().ToCharArray()
|> Array.map (fun c -> int(c.ToString()))

// get the sum of the factorials of a number's digits
let getDigitsToFactSum (n:bigint) =
bigint(getDigits(n) |> Array.map (fun n -> factorials.[n]) |> Array.sum)

// get the max sum achievable by a number of the given number of digits
let upperBound (digits:int) = bigint(digits) * bigint(factorial 9)

// find the last number of digits n, where the max sum achievable by the factorials of the
// digits of a number of n digits is greater than the smallest number of n digits
// any number with more than n digits do not need to be checked
let digitsToCheck =
let n =
Seq.unfold (fun state -> Some(state, (state+1))) 1
|> Seq.filter (fun x -> (upperBound x).ToString().ToCharArray().Length < x)