49 lines
964 B
Markdown
49 lines
964 B
Markdown
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---
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id: 5900f5241000cf542c510037
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title: 'Problem 440: GCD and Tiling'
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challengeType: 5
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forumTopicId: 302112
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dashedName: problem-440-gcd-and-tiling
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---
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# --description--
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We want to tile a board of length n and height 1 completely, with either 1 × 2 blocks or 1 × 1 blocks with a single decimal digit on top:
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For example, here are some of the ways to tile a board of length n = 8:
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Let T(n) be the number of ways to tile a board of length n as described above.
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For example, T(1) = 10 and T(2) = 101.
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Let S(L) be the triple sum ∑a,b,c gcd(T(ca), T(cb)) for 1 ≤ a, b, c ≤ L. For example: S(2) = 10444 S(3) = 1292115238446807016106539989 S(4) mod 987 898 789 = 670616280.
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Find S(2000) mod 987 898 789.
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# --hints--
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`euler440()` should return 970746056.
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```js
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assert.strictEqual(euler440(), 970746056);
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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 euler440() {
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return true;
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}
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euler440();
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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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