EulerProj_1.fs

(*
    Problem 1
    If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
    Find the sum of all the multiples of 3 or 5 below 1000.
*)
let problem_1 n =
    let mutable result = 0
    let rec loop n r = 
        if n = 0 then r
        else
            if (n % 3 = 0) || (n % 5 = 0) then loop (n-1) r + n
            else loop (n-1) r
    
    loop (n-1) result

//clever but lazy one, with lists comprehensions (not mine):
let problem_1a = 
    ([3..3..1000]@[5..5..999] |> List.sum) - ([15..15..1000] |> List.sum)

//super, from pdf attached to problem:
let problem_1b target =
    let sum (n) = 
        let p = target / n
        n*(p*(p+1)) / 2

    (sum 3) + (sum 5) - (sum 15)