---
id: 5900f49f1000cf542c50ffb1
challengeType: 5
title: 'Problem 306: Paper-strip Game'
---
## 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?
## Instructions
## Tests
```yml
tests:
- text: euler306() should return 852938.
testString: 'assert.strictEqual(euler306(), 852938, ''euler306() should return 852938.'');'
```
## Challenge Seed
```js
function euler306() {
// Good luck!
return true;
}
euler306();
```