---
id: 5900f38b1000cf542c50fe9e
challengeType: 5
title: 'Problem 31: Coin sums'
---

## Description
<section id='description'>
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 £(n) be made using any number of coins?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>coinSums(50)</code> should return 451.
    testString: 'assert(coinSums(50) == 451, ''<code>coinSums(50)</code> should return 451.'');'
  - text: <code>coinSums(100)</code> should return 4563.
    testString: 'assert(coinSums(100) == 4563, ''<code>coinSums(100)</code> should return 4563.'');'
  - text: <code>coinSums(150)</code> should return 21873.
    testString: 'assert(coinSums(150) == 21873, ''<code>coinSums(150)</code> should return 21873.'');'
  - text: <code>coinSums(200)</code> should return 73682.
    testString: 'assert(coinSums(200) == 73682, ''<code>coinSums(200)</code> should return 73682.'');'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function coinSums(n) {
  // Good luck!
  return n;
}

coinSums(200);
```

</div>



</section>

## Solution
<section id='solution'>


```js
const coinSums = (n) => {
  const getWays = (n, m=8, c=[1, 2, 5, 10, 20, 50, 100, 200]) => {
    if (n === 0) return 1;
    if (m === 0 || n < 0) return 0;
    return getWays(n - c[m - 1], m, c) + getWays(n, m - 1, c);
  };
  return getWays(n);
};
```

</section>