Suppose that Galina and Vlada are playing a finitely repeated flag game. The game starts with seven flags in the ground, and the players take turns removing the flags. A player must remove either one, two, or three flags per turn. The player who takes the last flag out of the ground, whether it is by itself or in a group, wins the game. Assume that Galina decides first on how many flags to remove. How many flags should Galina remove on her first turn to guarantee that she will win the game? Use backward induction.
A) one
B) two
C) three
D) either one or two

Question

Quizplus · Accepted Answer

To guarantee a win, Galina needs to ensure that she leaves 4 flags for Vlada's turn after her second turn. This is because no matter how many flags Vlada removes (1, 2, or 3), Galina can then remove the remaining flags to win. To achieve this, Galina should remove 3 flags on her first turn, leaving 4 flags after her second turn regardless of Vlada's actions.

Suppose That Galina and Vlada Are Playing a Finitely Repeated