freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/department-numbers.english.md

---
title: Department Numbers
id: 59f40b17e79dbf1ab720ed7a
challengeType: 5
forumTopicId: 302249
---

## Description
<section id='description'>
There is a highly organized city that has decided to assign a number to each of their departments:
<ul>
  <li>Police department</li>
  <li>Sanitation department</li>
  <li>Fire department</li>
</ul>
Each department can have a number between 1 and 7  (inclusive).
The three department numbers are to be unique (different from each other) and must add up to the number 12.
The Chief of the Police doesn't like odd numbers and wants to have an even number for his department.
</section>

## Instructions
<section id='instructions'>
Write a program which outputs all valid combinations as an array.

```js
[2, 3, 7] [2, 4, 6] [2, 6, 4]
[2, 7, 3] [4, 1, 7] [4, 2, 6]
[4, 3, 5] [4, 5, 3] [4, 6, 2]
[4, 7, 1] [6, 1, 5] [6, 2, 4]
[6, 4, 2] [6, 5, 1]
```

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>combinations</code> should be a function.
    testString: assert(typeof combinations === 'function');
  - text: <code>combinations([1, 2, 3], 6)</code> should return an Array.
    testString: assert(Array.isArray(combinations([1, 2, 3], 6)));
  - text: <code>combinations([1, 2, 3, 4, 5, 6, 7], 12)</code> should return an array of length 14.
    testString: assert(combinations(nums, total).length === len);
  - text: <code>combinations([1, 2, 3, 4, 5, 6, 7], 12)</code> should return all valid combinations.
    testString: assert.deepEqual(combinations(nums, total), result);

```

</section>

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

<div id='js-seed'>

```js
function combinations(possibleNumbers, total) {
  // Good luck!
  return true;
}
```

</div>


### After Test
<div id='js-teardown'>

```js
const nums = [1, 2, 3, 4, 5, 6, 7];
const total = 12;
const len = 14;
const result = [
  [2, 3, 7],
  [2, 4, 6],
  [2, 6, 4],
  [2, 7, 3],
  [4, 1, 7],
  [4, 2, 6],
  [4, 3, 5],
  [4, 5, 3],
  [4, 6, 2],
  [4, 7, 1],
  [6, 1, 5],
  [6, 2, 4],
  [6, 4, 2],
  [6, 5, 1]
];
```

</div>

</section>

## Solution
<section id='solution'>


```js
function combinations(possibleNumbers, total) {
  let firstNumber;
  let secondNumber;
  let thridNumber;
  const allCombinations = [];

  for (let i = 0; i < possibleNumbers.length; i += 1) {
    firstNumber = possibleNumbers[i];

    if (firstNumber % 2 === 0) {
      for (let j = 0; j < possibleNumbers.length; j += 1) {
        secondNumber = possibleNumbers[j];

        if (j !== i && firstNumber + secondNumber <= total) {
          thridNumber = total - firstNumber - secondNumber;

          if (thridNumber !== firstNumber && thridNumber !== secondNumber && possibleNumbers.includes(thridNumber)) {
            allCombinations.push([firstNumber, secondNumber, thridNumber]);
          }
        }
      }
    }
  }
  return allCombinations;
}

```

</section>