Question 1
Stekel and Prik play a game on an $m\times n$ board, where $m,n$ are positive integers. They take turns, with Stekel going first. On each turn, Stekel places a pawn on an unoccupied square. Prik does the same on his turn, but his chosen square must share a side with the square where Stekel placed his pawn on the immediately preceding turn. Prik wins when the whole board is filled with pawns. Stekel wins if Prik cannot place a pawn on his turn while at least one square is still empty. Determine, for every pair $(m,n)$, which player has a winning strategy.