---
id: 5900f41a1000cf542c50ff2c
title: >-
  Problem 173: Using up to one million tiles how many different "hollow" square
  laminae can be formed?
challengeType: 1
forumTopicId: 301808
dashedName: >-
  problem-173-using-up-to-one-million-tiles-how-many-different-hollow-square-laminae-can-be-formed
---

# --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:

<img alt="two square lamina with holes 2x2 and 7x7" src="https://cdn.freecodecamp.org/curriculum/project-euler/using-up-to-one-million-tiles-how-many-different-hollow-square-laminae-can-be-formed.gif" style="background-color: white; padding: 10px; display: block; margin-right: auto; margin-left: auto; margin-bottom: 1.2rem;">

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?

# --hints--

`differentHollowSquareLaminae()` should return `1572729`.

```js
assert.strictEqual(differentHollowSquareLaminae(), 1572729);
```

# --seed--

## --seed-contents--

```js
function differentHollowSquareLaminae() {

  return true;
}

differentHollowSquareLaminae();
```

# --solutions--

```js
// solution required
```
