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

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--

`euler173()` should return 1572729.

```js
assert.strictEqual(euler173(), 1572729);
```

# --seed--

## --seed-contents--

```js
function euler173() {

  return true;
}

euler173();
```

# --solutions--

```js
// solution required
```
