Problem

A variation of the game of Nim begins with a pile of sticks, from which a player can remove 1, 2, or 3 sticks at each turn. The player must remove at least 1 (but no more than remain on the pile). The player who takes the last stick loses. Draw the complete game tree that begins with (a) 5 sticks (b) 6 sticks. Assign appropriate values for the leaves of the tree, and evaluate the other nodes by the minimax method.