49 lines
865 B
Markdown
49 lines
865 B
Markdown
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---
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id: 5900f5061000cf542c510017
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title: 'Problem 409: Nim Extreme'
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challengeType: 5
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forumTopicId: 302077
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dashedName: problem-409-nim-extreme
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---
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# --description--
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Let n be a positive integer. Consider nim positions where:There are n non-empty piles.
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Each pile has size less than 2n.
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No two piles have the same size.
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Let W(n) be the number of winning nim positions satisfying the above
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conditions (a position is winning if the first player has a winning strategy). For example, W(1) = 1, W(2) = 6, W(3) = 168, W(5) = 19764360 and W(100) mod 1 000 000 007 = 384777056.
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Find W(10 000 000) mod 1 000 000 007.
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# --hints--
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`euler409()` should return 253223948.
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```js
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assert.strictEqual(euler409(), 253223948);
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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 euler409() {
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return true;
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}
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euler409();
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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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