45 lines
964 B
Markdown
45 lines
964 B
Markdown
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---
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id: 5900f4b11000cf542c50ffc3
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title: 'Problem 324: Building a tower'
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challengeType: 5
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forumTopicId: 301981
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dashedName: problem-324-building-a-tower
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---
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# --description--
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Let $f(n)$ represent the number of ways one can fill a $3×3×n$ tower with blocks of $2×1×1$. You're allowed to rotate the blocks in any way you like; however, rotations, reflections etc of the tower itself are counted as distinct.
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For example (with $q = 100\\,000\\,007$):
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$$\begin{align} & f(2) = 229, \\\\ & f(4) = 117\\,805, \\\\ & f(10)\bmod q = 96\\,149\\,360, \\\\ & f({10}^3)\bmod q = 24\\,806\\,056, \\\\ & f({10}^6)\bmod q = 30\\,808\\,124. \end{align}$$
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Find $f({10}^{10000})\bmod 100\\,000\\,007$.
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# --hints--
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`buildingTower()` should return `96972774`.
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```js
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assert.strictEqual(buildingTower(), 96972774);
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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 buildingTower() {
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return true;
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}
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buildingTower();
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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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