1.4 KiB
id | title | challengeType | forumTopicId |
---|---|---|---|
5900f49f1000cf542c50ffb1 | Problem 306: Paper-strip Game | 5 | 301960 |
--description--
The following game is a classic example of Combinatorial Game Theory:
Two players start with a strip of n white squares and they take alternate turns. On each turn, a player picks two contiguous white squares and paints them black. The first player who cannot make a move loses.
If n = 1, there are no valid moves, so the first player loses automatically. If n = 2, there is only one valid move, after which the second player loses. If n = 3, there are two valid moves, but both leave a situation where the second player loses. If n = 4, there are three valid moves for the first player; she can win the game by painting the two middle squares. If n = 5, there are four valid moves for the first player (shown below in red); but no matter what she does, the second player (blue) wins.
So, for 1 ≤ n ≤ 5, there are 3 values of n for which the first player can force a win. Similarly, for 1 ≤ n ≤ 50, there are 40 values of n for which the first player can force a win.
For 1 ≤ n ≤ 1 000 000, how many values of n are there for which the first player can force a win?
--hints--
euler306()
should return 852938.
assert.strictEqual(euler306(), 852938);
--seed--
--seed-contents--
function euler306() {
return true;
}
euler306();
--solutions--
// solution required