KöMaL 2014 A620

Arthur and Ben have a chocolate table of size $k\times n$ , they play a game with this chocolate. They alternately eat parts of the chocolate; Arthur is first. In every step, the current player breaks the chocolate table into two rectangular parts along the lines and eats up the smaller part. (If eventually the two pieces are equal, he can choose which part to eat.) The player who first eats a single chocolate square in a step loses, the other player wins. Determine all pairs $(k,n)$ for which Arthur has a winning strategy.