78 lines
1.3 KiB
Markdown
78 lines
1.3 KiB
Markdown
---
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id: 5900f38b1000cf542c50fe9e
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title: 'Problem 31: Coin sums'
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challengeType: 5
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forumTopicId: 301965
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dashedName: problem-31-coin-sums
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---
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# --description--
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In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:
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<div style='margin-left: 4em;'>1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).</div>
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It is possible to make £2 in the following way:
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<div style='margin-left: 4em;'>1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p</div>
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How many different ways can `n` pence be made using any number of coins?
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# --hints--
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`coinSums(50)` should return a number.
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```js
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assert(typeof coinSums(50) === 'number');
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```
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`coinSums(50)` should return 451.
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```js
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assert(coinSums(50) == 451);
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```
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`coinSums(100)` should return 4563.
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```js
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assert(coinSums(100) == 4563);
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```
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`coinSums(150)` should return 21873.
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```js
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assert(coinSums(150) == 21873);
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```
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`coinSums(200)` should return 73682.
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```js
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assert(coinSums(200) == 73682);
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```
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# --seed--
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## --seed-contents--
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```js
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function coinSums(n) {
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return n;
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}
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coinSums(200);
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```
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# --solutions--
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```js
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const coinSums = (n) => {
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const getWays = (n, m=8, c=[1, 2, 5, 10, 20, 50, 100, 200]) => {
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if (n === 0) return 1;
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if (m === 0 || n < 0) return 0;
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return getWays(n - c[m - 1], m, c) + getWays(n, m - 1, c);
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};
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return getWays(n);
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};
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```
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