There are two players 1 and 2, and the game begins with player 1 selecting one of the boxes marked 1 to 16. Following such a selection, the selected box, as well as all boxes in the square of which the selected box constitutes the leftmost and lowest corner, will be deleted. For example, if he selects box 7, then all the boxes, 3, 4, 7 and 8 are deleted. Similarly, if he selects box 9, then all boxes 1 to 12 are deleted. Next it is player 2’s turn to select a box from the remaining boxes. The same deletion rule applies in this case. It is then player 1’s turn again, and so on. Whoever deletes the last box loses the game? What is a winning strategy for player 1 in this game?
I can't even begin to form a payoff matrix or anything for this question, do we have to consider ALL the possible alternatives?