45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
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---
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id: 5900f41a1000cf542c50ff2d
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title: >-
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Problem 174: Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements
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challengeType: 5
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forumTopicId: 301809
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dashedName: >-
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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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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). Let N(n) be the number of t ≤ 1000000 such that t is type L(n); for example, N(15) = 832. What is ∑ N(n) for 1 ≤ n ≤ 10?
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# --hints--
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`euler174()` should return 209566.
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```js
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assert.strictEqual(euler174(), 209566);
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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 euler174() {
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return true;
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}
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euler174();
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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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