54 lines
1.7 KiB
Markdown
54 lines
1.7 KiB
Markdown
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---
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id: 5900f4991000cf542c50ffab
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title: 'Problem 301: Nim'
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challengeType: 5
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forumTopicId: 301955
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dashedName: problem-301-nim
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---
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# --description--
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Nim is a game played with heaps of stones, where two players take it in turn to remove any number of stones from any heap until no stones remain.
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We'll consider the three-heap normal-play version of Nim, which works as follows:
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- At the start of the game there are three heaps of stones.
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- On his turn the player removes any positive number of stones from any single heap.
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- The first player unable to move (because no stones remain) loses.
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If (n1,n2,n3) indicates a Nim position consisting of heaps of size n1, n2 and n3 then there is a simple function X(n1,n2,n3) — that you may look up or attempt to deduce for yourself — that returns: zero if, with perfect strategy, the player about to move will eventually lose; or non-zero if, with perfect strategy, the player about to move will eventually win. For example X(1,2,3) = 0 because, no matter what the current player does, his opponent can respond with a move that leaves two heaps of equal size, at which point every move by the current player can be mirrored by his opponent until no stones remain; so the current player loses. To illustrate:
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- current player moves to (1,2,1)
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- opponent moves to (1,0,1)
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- current player moves to (0,0,1)
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- opponent moves to (0,0,0), and so wins.
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For how many positive integers n ≤ 230 does X(n,2n,3n) = 0 ?
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# --hints--
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`euler301()` should return 2178309.
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```js
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assert.strictEqual(euler301(), 2178309);
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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 euler301() {
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return true;
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}
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euler301();
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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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