freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-61-cyclical-figurate-numbers.md

---
id: 5900f3a91000cf542c50febc
challengeType: 5
title: 'Problem 61: Cyclical figurate numbers'
forumTopicId: 302173
---

## Description
<section id='description'>
Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:

|Type of Number|Formula|Sequence|
|--- |--- |--- |
|Triangle|P<sub>3</sub>,<var><sub>n</sub></var>=<var>n</var>(<var>n</var>+1)/2|1, 3, 6, 10, 15, ...|
|Square|P<sub>4</sub>,<var><sub>n</sub></var>=<var>n</var><sup>2</sup>|1, 4, 9, 16, 25, ...|
|Pentagonal|P<sub>5</sub>,<var><sub>n</sub></var>=<var>n</var>(3<var>n</var>−1)/2|1, 5, 12, 22, 35, ...|
|Hexagonal|P<sub>6</sub>,<var><sub>n</sub></var>=<var>n</var>(2<var>n</var>−1)|1, 6, 15, 28, 45, ...|
|Heptagonal|P<sub>7</sub>,<var><sub>n</sub></var>=<var>n</var>(5<var>n</var>−3)/2|1, 7, 18, 34, 55, ...|
|Octagonal|P<sub>8</sub>,<var><sub>n</sub></var>=<var>n</var>(3<var>n</var>−2)|1, 8, 21, 40, 65, ...|

The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.

<ol>
  <li>The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).</li>
  <li>Each polygonal type: triangle (P<sub>3,127</sub> = 8128), square (P<sub>4,91</sub> = 8281), and pentagonal (P<sub>5,44</sub> = 2882), is represented by a different number in the set.</li>
  <li>This is the only set of 4-digit numbers with this property.</li>
</ol>

Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set.

</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>cyclicalFigurateNums()</code> should return a number.
    testString: assert(typeof cyclicalFigurateNums() === 'number');
  - text: <code>cyclicalFigurateNums()</code> should return 28684.
    testString: assert.strictEqual(cyclicalFigurateNums(), 28684);

```

</section>

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

<div id='js-seed'>

```js
function cyclicalFigurateNums() {

  return true;
}

cyclicalFigurateNums();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>