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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-366-stone-game-iii.md

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+---
+id: 5900f4da1000cf542c50ffed
+challengeType: 5
+title: 'Problem 366: Stone Game III'
+forumTopicId: 302027
+---
+
+## Description
+<section id='description'>
+Two players, Anton and Bernhard, are playing the following game.
+There is one pile of n stones.
+The first player may remove any positive number of stones, but not the whole pile.
+Thereafter, each player may remove at most twice the number of stones his opponent took on the previous move.
+The player who removes the last stone wins.
+
+
+E.g. n=5
+If the first player takes anything more than one stone the next player will be able to take all remaining stones.
+If the first player takes one stone, leaving four, his opponent will take also one stone, leaving three stones.
+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.
+So 5 is a losing position for the first player.
+For some winning positions there is more than one possible move for the first player.
+E.g. when n=17 the first player can remove one or four stones.
+
+
+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.
+
+
+∑M(n) for n≤100 is 728.
+
+
+Find  ∑M(n) for n≤1018.
+Give your answer modulo 108.
+</section>
+
+## Instructions
+<section id='instructions'>
+
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>euler366()</code> should return 88351299.
+    testString: assert.strictEqual(euler366(), 88351299);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function euler366() {
+
+  return true;
+}
+
+euler366();
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+```js
+// solution required
+```
+
+</section>