# Project Euler – Problem 31 Solution

Yan Cui

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#### Problem

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:

1x£1 + 1x50p + 2x20p + 1x5p + 1x2p + 3x1p

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

#### Solution

```// the total and available coins
let total, coins = 200, [1;2;5;10;20;50;100;200]

// implement the coin change algorithm
let rec count n m =
if n = 0 then 1
else if n < 0 then 0
else if (m <= 0 && n >= 1) then 0
else (count n (m-1)) + (count (n-coins.[m-1]) m)

let answer = count total coins.Length
```

Not much for me to add here really, see here for the coin change algorithm which I’ve used in my solution.