Project Euler: Problem 16

It’s been a while since we last did any Project Euler problems, so why not have a go?

2¹⁵ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the sum of the digits of the number 2¹⁰⁰⁰?

Unfortunately, this is another one of those Euler problems that shows its age. While 2¹⁰⁰⁰ far exceeds the domain of 64-bit integers, it is nothing a modern numerics library can’t handle. In our case, we use F#’s BigInteger:

open System

let num = 2I ** 1000

We then convert this number to a string, and make a list of all the digits by parsing them one at the time:

let str = num.ToString()

let numList = [ for i in 0..str.Length - 1 do yield UInt64.Parse(str.[i].ToString()) ]

Now we simply take the sum of this list to arrive at the answer:

let result = numList |> List.sum

There are, unfortunately, no tricks involved this time.