#=
Created on 26 Sep 2021

@author: David Doblas Jiménez
@email: daviddoji@pm.me

Solution for Problem 53 of Project Euler
https://projecteuler.net/problem=53
=#

using BenchmarkTools
using Combinatorics

function Problem53()
    #=
    There are exactly ten ways of selecting three from five, 12345:

        123, 124, 125, 134, 135, 145, 234, 235, 245, and 345

    In combinatorics, we use the notation, (5 over 3) = 10.

    In general, (n over r) = n!/r!*(n-r)!, where r<=n, n!=n*(n-1)*...*2*1, and 0!=1.

    It is not until
    , that a value exceeds one-million: (23 over 10) = 1144066.

    How many, not necessarily distinct, values of (n over r) for 1<=n<=100, are greater than one-million?
    =#

    ans = 0
    for x in 1:100
        for y in 1:100
            if binomial(big(x), y) > 1_000_000
                ans += 1
            end
        end
    end

    return ans
end


println("Time to evaluate Problem $(lpad(53, 3, "0")):")
@btime Problem53()
println("")
println("Result for Problem $(lpad(53, 3, "0")): ", Problem53())