---
id: 5900f4801000cf542c50ff92
title: 'Problem 275: Balanced Sculptures'
challengeType: 5
forumTopicId: 301925
dashedName: problem-275-balanced-sculptures
---

# --description--

Let us define a balanced sculpture of order n as follows:

A polyomino made up of n+1 tiles known as the blocks (n tiles) and the plinth (remaining tile);

the plinth has its centre at position (x = 0, y = 0);

the blocks have y-coordinates greater than zero (so the plinth is the unique lowest tile);

the centre of mass of all the blocks, combined, has x-coordinate equal to zero.

When counting the sculptures, any arrangements which are simply reflections about the y-axis, are not counted as distinct. For example, the 18 balanced sculptures of order 6 are shown below; note that each pair of mirror images (about the y-axis) is counted as one sculpture:

There are 964 balanced sculptures of order 10 and 360505 of order 15.How many balanced sculptures are there of order 18?

# --hints--

`euler275()` should return 15030564.

```js
assert.strictEqual(euler275(), 15030564);
```

# --seed--

## --seed-contents--

```js
function euler275() {

  return true;
}

euler275();
```

# --solutions--

```js
// solution required
```