#= Created on 27 Aug 2021 @author: David Doblas Jiménez @email: daviddoji@pm.me Solution for Problem 31 of Project Euler https://projecteuler.net/problem=31 =# using BenchmarkTools using IterTools function Problem31() #= In the United Kingdom the currency is made up of pound (£) and pence (p). There are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, 50p, £1 (100p), and £2 (200p). It is possible to make £2 in the following way: 1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p How many different ways can £2 be made using any number of coins? =# no_ways = 0 coins = [2, 5, 10, 20, 50, 100] bunch_of_coins = product([0:i:200 for i in coins]...) for money in bunch_of_coins if sum(money) <= 200 no_ways += 1 end end # consider also the case for 200 coins of 1p return no_ways + 1 end println("Time to evaluate Problem 31:") @btime Problem31() println("") println("Result for Problem 31: ", Problem31())