Problem 31 : Coin sums

Problem Statement

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?

Solution

coins = [1, 2, 5, 10, 20, 50, 100, 200]
ways = [1] + [0]*200

for coin in coins:
    for i in range(coin,201):
        ways[i] += ways[i-coin]
print(ways[200])

Output

73682