Difference between revisions of "2004 AMC 12A Problems/Problem 7"
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Therefore, after 12 sets of 3 rounds, or 36 rounds, the players will have 3, 2, and 1 tokens, repectively. After 1 more round, player <math>A</math> will give away his last 3 tokens and the game will stop <math>\Rightarrow\mathrm{(B)}</math>. | Therefore, after 12 sets of 3 rounds, or 36 rounds, the players will have 3, 2, and 1 tokens, repectively. After 1 more round, player <math>A</math> will give away his last 3 tokens and the game will stop <math>\Rightarrow\mathrm{(B)}</math>. | ||
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Revision as of 01:39, 11 September 2007
Problem
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 in the discard pile. The game ends when some player runs out of tokens. Players 
, 
, and 
start with 15, 14, and 13 tokens, respectively. How many rounds will there be in the game?
Solution
Look at a set of 3 rounds, where the players have 
, 
, and 
tokens. Each of the players will gain two tokens from the others and give away 3 tokens, so overall, each player will lose 1 token.
Therefore, after 12 sets of 3 rounds, or 36 rounds, the players will have 3, 2, and 1 tokens, repectively. After 1 more round, player will give away his last 3 tokens and the game will stop 
.
See also
| 2004 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
