(*
    Problem 6

    The sum of the squares of the first ten natural numbers is,
        12 + 22 + ... + 102 = 385
    The square of the sum of the first ten natural numbers is,
        (1 + 2 + ... + 10)2 = 552 = 3025
    Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025  385 = 2640.
    Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.


    (a + b + c + d + e)^2 =a^2 + b^2 + c^2 + d^2 + e^2 + 2a(b + c + d + e) + 2b(c + d + e) + 2c(d + e) + 2de
*)

let problem_6 n =
    let rec loop result tempsum n =
        printfn "N = %i" n
        printfn "result = %i" result
        printfn "tempsum = %i" tempsum
        if n <=1 then result
        else
            let newTempsum = tempsum + n
            printfn "newTempsum = %i" newTempsum
            loop (result + (2*(n-1) * newTempsum)) newTempsum (n-1)

    loop 0 0 n
problem_6 100 |> ignore