# A Fair Game?

Probability Level 3

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?

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