Question 18
A game is played on an $n \times n$ chessboard. At the beginning there are 99 stones on each square. Two players $A$ and $B$ take turns, where in each turn the player chooses either a row or a column and removes one stone from each square in the chosen row or column. They are only allowed to choose a row or a column, if it has at least one stone on each square. The first player who cannot move, loses the game. Player $A$ takes the first turn. Determine all $n$ for which player $A$ has a winning strategy.