1af6e7aa5a
* fix: clean-up Project Euler 321-340 * fix: typo * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
51 lines
1.6 KiB
Markdown
51 lines
1.6 KiB
Markdown
---
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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. On each player's turn, the player may remove a number of stones from the larger pile. The number of stones 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 ($x_i + y_i$) for all losing configurations ($x_i$, $y_i$), $0 < x_i < y_i ≤ N$. We can verify that $S(10) = 211$ and $S({10}^4) = 230\\,312\\,207\\,313$.
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Find $S({10}^{16})\bmod 7^{10}$.
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# --hints--
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`stoneGameTwo()` should return `54672965`.
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```js
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assert.strictEqual(stoneGameTwo(), 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 stoneGameTwo() {
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return true;
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}
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stoneGameTwo();
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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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