4. One variation on the game of nim is described in Luger. 7 The game begins with a single pile of stones. The move by a player consists of dividing a pile into two piles that contain an unequal number of stones. For example, if one pile contains six stones, it could be subdivided into piles of five and one, or four and two, but not three and three. The first player who cannot make a move loses the game.

a. Draw the complete game tree for this version of Nim if the start state consists of six stones.

b. Perform a minimax evaluation for this game. Let 1 denote a win and 0 a loss.