Question 16
There are given $2k$ boxes ($k \ge 2$) with $2k-1$ pebbles in each one. A legal move is to choose $2k-2$ boxes and remove one pebble from each one of them. Players $A$ and $B$ make moves alternately; $A$ goes first. A player wins if a move of his empties two boxes. Determine which player has a winning strategy.