2004 AMC 12A Problem 7
Attempt Problem 7 of the 2004 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12A solutions, or check the answer key.
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7.
A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token into a discard pile. The game ends when some player runs out of tokens. Players and start with and tokens, respectively. How many rounds will there be in the game?
Answer: B
Solution:
After three rounds the players and have and tokens, respectively. Every subsequent three rounds reduces each player's supply by one token.
After rounds they have and tokens. In the th round player who has the most, gives away all three of their tokens and runs out, ending the game.
Thus, the correct answer is B.
Problem 7 in Other Years
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