Empty, remove 0, 1, or 2, and divide Consider the following impartial combinatorial game. Two boxes each contain a nonzero number of chips. Two player alternate turns. A turn consists of a player choosing a box and emptying it, removing 0, 1, or 2 chips from the pile in the other box, then dividing the remaining chips so that both boxes again have a nonzero number of chips. Thus, (1, 1) is the only terminal position. Find a description of the P-positions for this game. You must justify your answer. Hint: You may find the solution to the third problem on the midterm to be helpful.