Suppose that Ben and Tim are playing a finitely repeated flag game. The game starts with 7 flags in the ground, and the players take turns removing the flags. A player must remove either 1, 2, or 3 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 Ben decides first on how many flags to remove. How many flags should Ben remove on his first turn to guarantee that he will win the game? Use backward induction.
A) 1
B) 2
C) 3
D) either 1 or 2

Question

Quizplus · Accepted Answer

By removing 3 flags on his first turn, Ben leaves 4 flags for Tim. No matter how many flags Tim removes (1, 2, or 3), Ben can always adjust his next move to leave a losing position for Tim, ensuring Ben wins.

Suppose That Ben and Tim Are Playing a Finitely Repeated