52 lines
1.5 KiB
Markdown
52 lines
1.5 KiB
Markdown
---
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id: 5900f4801000cf542c50ff92
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title: 'Problem 275: Balanced Sculptures'
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challengeType: 5
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forumTopicId: 301925
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dashedName: problem-275-balanced-sculptures
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---
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# --description--
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Let us define a balanced sculpture of order $n$ as follows:
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- A polyomino made up of $n + 1$ tiles known as the blocks ($n$ tiles) and the plinth (remaining tile);
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- the plinth has its centre at position ($x = 0$, $y = 0$);
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- the blocks have $y$-coordinates greater than zero (so the plinth is the unique lowest tile);
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- the centre of mass of all the blocks, combined, has $x$-coordinate equal to zero.
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When counting the sculptures, any arrangements which are simply reflections about the $y$-axis, are <u>not</u> 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:
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<img class="img-responsive center-block" alt="18 balanced sculptures of order 6" src="https://cdn.freecodecamp.org/curriculum/project-euler/balanced-sculptures.gif" style="background-color: white; padding: 10px;">
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There are 964 balanced sculptures of order 10 and 360505 of order 15.
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How many balanced sculptures are there of order 18?
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# --hints--
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`balancedSculptures()` should return `15030564`.
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```js
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assert.strictEqual(balancedSculptures(), 15030564);
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```
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# --seed--
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## --seed-contents--
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```js
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function balancedSculptures() {
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return true;
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}
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balancedSculptures();
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```
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# --solutions--
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```js
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// solution required
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```
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