Solution to Problem 31, written in Python.

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?

count = 0

for two_pounds in range(200, -1, -200):
	for one_pound in range(two_pounds, -1, -100):
		for fifty_pence in range(one_pound, -1, -50):
			for twenty_pence in range(fifty_pence, -1, -20):
				for ten_pence in range(twenty_pence, -1, -10):
					for five_pence in range(ten_pence, -1, -5):
						for two_pence in range(five_pence, -1, -2):
							count += 1

print count