49 lines
908 B
Markdown
49 lines
908 B
Markdown
---
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id: 5900f5021000cf542c510014
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title: 'Problem 405: A rectangular tiling'
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challengeType: 5
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forumTopicId: 302073
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dashedName: problem-405-a-rectangular-tiling
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---
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# --description--
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We wish to tile a rectangle whose length is twice its width.
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Let T(0) be the tiling consisting of a single rectangle.
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For n > 0, let T(n) be obtained from T(n-1) by replacing all tiles in the following manner:
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The following animation demonstrates the tilings T(n) for n from 0 to 5:
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Let f(n) be the number of points where four tiles meet in T(n). For example, f(1) = 0, f(4) = 82 and f(109) mod 177 = 126897180.
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Find f(10k) for k = 1018, give your answer modulo 177.
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# --hints--
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`euler405()` should return 237696125.
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```js
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assert.strictEqual(euler405(), 237696125);
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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 euler405() {
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return true;
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}
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euler405();
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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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