Question 166
Let $n\gt 3$ be an integer which is not divisible by $3$. Two players $A$ and $B$ play the following game with an $n \times n$ chocolate table. First, player $A$ has to choose and remove one piece of the chocolate, without breaking other pieces. After his move, player $B$ tries to partition the remaining chocolate into $3 \times 1$ (and $1 \times 3$) rectangles. If $B$ manages to do so, then he/she is the winner. Otherwise the winner is $A$. Determine which player has a winning strategy and describe the strategy.