81 lines
1.8 KiB
Markdown
81 lines
1.8 KiB
Markdown
---
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id: 5900f4da1000cf542c50ffed
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challengeType: 5
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title: 'Problem 366: Stone Game III'
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forumTopicId: 302027
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---
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## Description
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<section id='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 2x1=2 stones. So let's say he takes also one stone, leaving 2. 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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∑M(n) for n≤100 is 728.
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Find ∑M(n) for n≤1018.
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Give your answer modulo 108.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler366()</code> should return 88351299.
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testString: assert.strictEqual(euler366(), 88351299);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler366() {
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// Good luck!
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return true;
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}
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euler366();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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