# Euler Solution 31

### From ProgSoc Wiki

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).

How many different ways can £2 be made using any number of coins?

# Solutions for Problem 31

## Python by Althalus

Runtime: 18 seconds

#Attempts to recursively work out the total number of ways one can make total from a certain start coin #increased everything by 100 to lose decimals. def twopounds(total,nextcoin): count = 0 coins = [ 1, 2, 5, 10, 20, 50, 100, 200 ] if total-nextcoin == 0: return 1 elif total-nextcoin < 0: return 0 elif total-nextcoin > 0: num = max([i for i,k in enumerate(coins) if k <= nextcoin]) for i in coins[:int(num+1)]: count += twopounds(total-nextcoin,i) return count return total total = 0 #Work out the total number of ways for each starting denomination. Add them together. Should be our total. total +=twopounds(200,200) total +=twopounds(200,100) total +=twopounds(200,50) total +=twopounds(200,20) total +=twopounds(200,10) total +=twopounds(200,5) total +=twopounds(200,2) total +=twopounds(200,1) print(total)