32fac23a2d
* fix: clean-up Project Euler 161-180 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
52 lines
1.6 KiB
Markdown
52 lines
1.6 KiB
Markdown
---
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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,
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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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<img class="img-responsive center-block" alt="two square lamina with holes 2x2 and 7x7" src="https://cdn.freecodecamp.org/curriculum/project-euler/using-up-to-one-million-tiles-how-many-different-hollow-square-laminae-can-be-formed.gif" style="background-color: white; padding: 10px;">
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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 $\sum N(n)$ for $1 ≤ n ≤ 10$?
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# --hints--
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`hollowSquareLaminaeDistinctArrangements()` should return `209566`.
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```js
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assert.strictEqual(hollowSquareLaminaeDistinctArrangements(), 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 hollowSquareLaminaeDistinctArrangements() {
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return true;
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}
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hollowSquareLaminaeDistinctArrangements();
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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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