# A Fair Game?

**Discrete Mathematics**Level 4

Mursalin and Trevor decide to play a game where Trevor gets to pick any positive integer \(n<1000\).

After that the game begins.

First Mursalin names an integer \(x\) from \(1\) to \(n\) [both inclusive]. Then Trevor has to name an integer from \(1\) to \(n\) [both inclusive] that does not divide \(x\). Then it's Mursalin's turn again and so on. On each turn the player has to select an integer from \(1\) through \(n\) [both inclusive] that doesn't divide all the numbers selected so far. The first person unable to name an integer under these constraints loses. Assuming that both players play optimally, for how many \(n\)'s does Mursalin have a winning strategy?