Suppose in the Wythoff’s game there are 40 matches in the first pile and 20 in the second pile and it is your turn to play. How would you play?

Please assist in how to complete this problem.

  • $\begingroup$ @TonyK any thoughts? $\endgroup$ – MathStudent2 Apr 9 at 3:38

$(20,12)$ is a safe pair so reduce the $40$ pile to $12$ and you win.

For a table of safe pairs see page 8 of this, e.g.

  • $\begingroup$ Is there a way to further explain this step by step as I have another similar problem? $\endgroup$ – MathStudent2 Apr 9 at 4:29
  • $\begingroup$ @MathStudent2 it’s trivial when you have the table. You lose iff you have to move in a “safe position” as that explanation calls it. Otherwise you move to a safe position and you win. There is a safe position with $20$ as the larger amount so that tells us what move to make. $\endgroup$ – Henno Brandsma Apr 9 at 4:49

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