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 into a 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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
After three rounds the players , and have 14, 13, and 12 tokens, respectively. Every subsequent three rounds of play reduces each player's supply of tokens by one. After 36 rounds they have 3, 2, and 1 token, respectively, and after the round Player has no tokens.
The problems on this page are the property of the MAA's American Mathematics Competitions