Consider the two-player subtraction game where the game starts at 20 and players are allowed to subtract 1, 3, or 6 from the previous amount on their turn with the goal of being the first to reach EXACTLY 0. (That is, you are not allowed to go into the negatives.)

Draw the vertices for the graph of this game (you may omit the edges as there are a lot of them), and then determine the kernel of this graph (see our notes or section 7.5 in the book for the definition of kernel; essentially these are the good vertices). Fully justify your reason for saying why these vertices are the good ones and determine which player (Player 1 or Player 2) has a winning strategy.