51 lines
1.2 KiB
Markdown
51 lines
1.2 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 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:
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There are 964 balanced sculptures of order 10 and 360505 of order 15.How many balanced sculptures are there of order 18?
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# --hints--
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`euler275()` should return 15030564.
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```js
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assert.strictEqual(euler275(), 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 euler275() {
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return true;
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}
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euler275();
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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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