Question 29
A game is played with two players and an initial stack of $n$ pennies ($n \geq 3$). The players take turns choosing one of the stacks of pennies on the table and splitting it into two stacks. The winner is the player who makes a move that causes all stacks to be of height 1 or 2. For which starting values of $n$ does the player who goes first win, assuming best play by both players?