1.8 KiB
id | challengeType | title |
---|---|---|
5900f4da1000cf542c50ffed | 5 | Problem 366: Stone Game III |
Description
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.
Instructions
Tests
tests:
- text: <code>euler366()</code> should return 88351299.
testString: assert.strictEqual(euler366(), 88351299, '<code>euler366()</code> should return 88351299.');
Challenge Seed
function euler366() {
// Good luck!
return true;
}
euler366();
Solution
// solution required