2004 AMC 10A Problem 8
Problem 8 of 25Easier
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 choices
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Solution
After the first three rounds the counts go from to In general, every three rounds each player loses exactly one token.
After rounds the counts are On the th round the leader gives away three tokens and drops to ending the game.
Thus, the correct answer is B.