7d9496e52c
* fix: clean-up Project Euler 361-380 * fix: improve wording Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: remove unnecessary paragraph * 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>
69 lines
1.7 KiB
Markdown
69 lines
1.7 KiB
Markdown
---
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id: 5900f4da1000cf542c50ffed
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title: 'Problem 366: Stone Game III'
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challengeType: 5
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forumTopicId: 302027
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dashedName: problem-366-stone-game-iii
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---
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# --description--
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Two players, Anton and Bernhard, are playing the following game.
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There is one pile of $n$ stones.
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The first player may remove any positive number of stones, but not the whole pile.
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Thereafter, each player may remove at most twice the number of stones his opponent took on the previous move.
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The player who removes the last stone wins.
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E.g. $n = 5$
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If the first player takes anything more than one stone the next player will be able to take all remaining stones.
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If the first player takes one stone, leaving four, his opponent will take also one stone, leaving three stones.
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The first player cannot take all three because he may take at most $2 \times 1 = 2$ stones. So let's say he also takes one stone, leaving 2.
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The second player can take the two remaining stones and wins.
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So 5 is a losing position for the first player.
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For some winning positions there is more than one possible move for the first player.
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E.g. when $n = 17$ the first player can remove one or four stones.
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Let $M(n)$ be the maximum number of stones the first player can take from a winning position at his first turn and $M(n) = 0$ for any other position.
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$\sum M(n)$ for $n ≤ 100$ is 728.
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Find $\sum M(n)$ for $n ≤ {10}^{18}$. Give your answer modulo ${10}^8$.
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# --hints--
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`stoneGameThree()` should return `88351299`.
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```js
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assert.strictEqual(stoneGameThree(), 88351299);
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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 stoneGameThree() {
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return true;
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}
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stoneGameThree();
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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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