63 lines
1.3 KiB
Markdown
63 lines
1.3 KiB
Markdown
---
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id: 5900f41a1000cf542c50ff2d
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challengeType: 5
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title: 'Problem 174: Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements'
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---
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## Description
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<section id='description'>
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We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry.
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Given eight tiles it is possible to form a lamina in only one way: 3x3 square with a 1x1 hole in the middle. However, using thirty-two tiles it is possible to form two distinct laminae.
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If t represents the number of tiles used, we shall say that t = 8 is type L(1) and t = 32 is type L(2).
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Let N(n) be the number of t ≤ 1000000 such that t is type L(n); for example, N(15) = 832.
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What is ∑ N(n) for 1 ≤ n ≤ 10?
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler174()</code> should return 209566.
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testString: assert.strictEqual(euler174(), 209566, '<code>euler174()</code> should return 209566.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler174() {
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// Good luck!
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return true;
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}
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euler174();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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