51 lines
1.5 KiB
Markdown
51 lines
1.5 KiB
Markdown
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---
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id: 5900f4b11000cf542c50ffc4
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title: 'Problem 325: Stone Game II'
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challengeType: 5
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forumTopicId: 301982
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dashedName: problem-325-stone-game-ii
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---
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# --description--
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A game is played with two piles of stones and two players. At her turn, a player removes a number of stones from the larger pile. The number of stones she removes must be a positive multiple of the number of stones in the smaller pile.
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E.g., let the ordered pair(6,14) describe a configuration with 6 stones in the smaller pile and 14 stones in the larger pile, then the first player can remove 6 or 12 stones from the larger pile.
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The player taking all the stones from a pile wins the game.
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A winning configuration is one where the first player can force a win. For example, (1,5), (2,6) and (3,12) are winning configurations because the first player can immediately remove all stones in the second pile.
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A losing configuration is one where the second player can force a win, no matter what the first player does. For example, (2,3) and (3,4) are losing configurations: any legal move leaves a winning configuration for the second player.
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Define S(N) as the sum of (xi+yi) for all losing configurations (xi,yi), 0 < xi < yi ≤ N. We can verify that S(10) = 211 and S(104) = 230312207313.
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Find S(1016) mod 710.
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# --hints--
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`euler325()` should return 54672965.
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```js
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assert.strictEqual(euler325(), 54672965);
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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 euler325() {
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return true;
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}
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euler325();
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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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