---
id: 5900f41a1000cf542c50ff2c
challengeType: 5
title: 'Problem 173: Using up to one million tiles how many different "hollow" square laminae can be formed?'
forumTopicId: 301808
---

## Description
<section id='description'>
We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry. For example, using exactly thirty-two square tiles we can form two different square laminae:


With one-hundred tiles, and not necessarily using all of the tiles at one time, it is possible to form forty-one different square laminae.
Using up to one million tiles how many different square laminae can be formed?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler173()</code> should return 1572729.
    testString: assert.strictEqual(euler173(), 1572729);

```

</section>

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

<div id='js-seed'>

```js
function euler173() {
  // Good luck!
  return true;
}

euler173();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>