51 lines
1.2 KiB
Markdown
51 lines
1.2 KiB
Markdown
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---
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id: 5900f5141000cf542c510027
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title: 'Problem 423: Consecutive die throws'
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challengeType: 5
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forumTopicId: 302093
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dashedName: problem-423-consecutive-die-throws
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---
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# --description--
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Let n be a positive integer.
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A 6-sided die is thrown n times. Let c be the number of pairs of consecutive throws that give the same value.
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For example, if n = 7 and the values of the die throws are (1,1,5,6,6,6,3), then the following pairs of consecutive throws give the same value: (1,1,5,6,6,6,3) (1,1,5,6,6,6,3) (1,1,5,6,6,6,3) Therefore, c = 3 for (1,1,5,6,6,6,3).
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Define C(n) as the number of outcomes of throwing a 6-sided die n times such that c does not exceed π(n).1 For example, C(3) = 216, C(4) = 1290, C(11) = 361912500 and C(24) = 4727547363281250000.
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Define S(L) as ∑ C(n) for 1 ≤ n ≤ L. For example, S(50) mod 1 000 000 007 = 832833871.
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Find S(50 000 000) mod 1 000 000 007.
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1 π denotes the prime-counting function, i.e. π(n) is the number of primes ≤ n.
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# --hints--
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`euler423()` should return 653972374.
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```js
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assert.strictEqual(euler423(), 653972374);
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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 euler423() {
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return true;
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}
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euler423();
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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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