# Multiply To Win

Alice and Betty are playing a game. Each turn, they choose a positive integer which hasn't been previously chosen. A player wins if, among the numbers that the player has chosen, there are three different numbers $a, b, c$ such that $ab = c$. (In particular, no player can win by having only chosen one or two numbers.)

Assuming perfect play, if Alice goes first, who has a winning strategy?

×