---
title: Count the coins
id: 59713bd26bdeb8a594fb9413
challengeType: 5
---

## Description
<section id='description'>
There are four types of common coins in <a href="https://en.wikipedia.org/wiki/United_States" title="link: https://en.wikipedia.org/wiki/United_States">US</a> currency:
<ul>
  <li>quarters (25 cents)</li>
  <li>dimes (10 cents)</li>
  <li>nickels (5 cents), and</li>
  <li>pennies (1 cent)</li>
</ul>
<p>There are six ways to make change for 15 cents:</p>
<ul>
  <li>A dime and a nickel</li>
  <li>A dime and 5 pennies</li>
  <li>3 nickels</li>
  <li>2 nickels and 5 pennies</li>
  <li>A nickel and 10 pennies</li>
  <li>15 pennies</li>
</ul>
Implement a function to determine how many ways there are to make change for a dollar using these common coins? (1 dollar = 100 cents)
<b>Reference:</b>
<ul>
  <li><a href="http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-11.html#%_sec_Temp_52" title="link: http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-11.html#%_sec_Temp_52">an algorithm from MIT Press</a>.</li>
</ul>
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>countCoins</code> is a function.
    testString: assert(typeof countCoins === 'function', '<code>countCoins</code> is a function.');
  - text: <code>countCoints()</code> should return 242.
    testString: assert.equal(countCoins(), 242, '<code>countCoints()</code> should return 242.');

```

</section>

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

<div id='js-seed'>

```js
function countCoins () {
  // Good luck!
  return true;
}
```

</div>



</section>

## Solution
<section id='solution'>


```js
function countCoins () {
  let t = 100;
  const operands = [1, 5, 10, 25];
  const targetsLength = t + 1;
  const operandsLength = operands.length;
  t = [1];

  for (let a = 0; a < operandsLength; a++) {
    for (let b = 1; b < targetsLength; b++) {
      // initialise undefined target
      t[b] = t[b] ? t[b] : 0;

      // accumulate target + operand ways
      t[b] += (b < operands[a]) ? 0 : t[b - operands[a]];
    }
  }

  return t[targetsLength - 1];
}

```

</section>