# Euler Solution 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).

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

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)
```