# ###
# Coin sums
# Problem 31
# 
# In England the currency is made up of pound, £, and pence, p, and 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?
# ###


coins = [200, 100, 50, 20, 10, 5, 2, 1]
solutions = []

def backtrack(n, sol):
    if sum(sol) > n:
        return
    if n == 0:
        solutions.append(sol)
        return
    while next_sol(n, sol):
        backtrack(n, sol)

def next_(n, sol):


backtrack(10, [])