47 lines
1.1 KiB
Markdown
47 lines
1.1 KiB
Markdown
---
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id: 5900f4291000cf542c50ff3c
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title: 'Problem 189: Tri-colouring a triangular grid'
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challengeType: 5
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forumTopicId: 301825
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dashedName: problem-189-tri-colouring-a-triangular-grid
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---
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# --description--
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Consider the following configuration of 64 triangles:
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We wish to colour the interior of each triangle with one of three colours: red, green or blue, so that no two neighbouring triangles have the same colour. Such a colouring shall be called valid. Here, two triangles are said to be neighbouring if they share an edge. Note: if they only share a vertex, then they are not neighbours.
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For example, here is a valid colouring of the above grid:
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A colouring C' which is obtained from a colouring C by rotation or reflection is considered distinct from C unless the two are identical.
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How many distinct valid colourings are there for the above configuration?
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# --hints--
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`euler189()` should return 10834893628237824.
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```js
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assert.strictEqual(euler189(), 10834893628237824);
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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 euler189() {
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return true;
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}
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euler189();
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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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