I am struggling to conceptually understand a question in a programming assignment for an algorithms class.

The problem is dealing with a fictitious 2 player game, named Easy. The rules of the game are simple; each player may chose one of 4 integers {0-3} after which that integer is not available for the other player. The catch is, a player picks {0} it means they quit.

The objective is for Player 1 to get {1} and Player 2 to get {2}, in which case they may win, however if both or neither succeed, then the game ends in a draw.

I have been asked to draw the game tree for Easy, showing all nodes, which they explained as 4! = 24. Labeling the edges, which represent moves (selecting a number) and the leaves with who won (1 means Player 1 won, -1 means Player 2 won, and 0 means a tie).

I have drawn out a game tree, which I believe is correct, however I am not 100% certain hence I am asking the question. My game tree only has 16 leaves. I am thinking that when a player picks {0}, and then quits, the game tree stops there? I don't see how it is possible to get to 24 leaves?

Any help would be greatly appreciate, and if you need more information I would be happy to provide it.

Thanks