Two teams participate in a competition of \"A Game of 31\". In this contest, 31

Question

Two teams participate in a competition of "A Game of 31". In this contest, 31 flags are placed in a circle, and the two teams take turns removing either 1, 2, or 3 flags from the circle. The team who removes the last flag (or flags) wins the game. Is there a winning strategy [1] for "A Game of 31"? Explain. Try to come up with a solution that works for any number of flags.

Try to experiment with coins or tokens instead of flags and play the game.

[1] A winning strategy is a way to play the game such that, whatever the opponent's moves are, the player is sure to win the game.

Explanation / Answer

The winning strategy is the first team should remove 3 flags from 31 flags in their first step. Now the number of flags are 28, which is a multiple of four. Now whatever the number of flags the second team removes, the first team then should remove (4-n) number of flags. For each round the number of flags removed by team 2 + number of flags removed by team 1 = n + (4-n) = 4 The first team will definitely get the chance to Win.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.