AMC10 2004 A

AMC10 2004 A · Q8

AMC10 2004 A · Q8. It mainly tests Arithmetic misc, Patterns & sequences (misc).

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 A, B, and C start with 15, 14, and 13 tokens, respectively. How many rounds will there be in the game?

一个游戏使用筹码，按照以下规则进行。每轮中，筹码最多的玩家给每个其他玩家一个筹码，并将一个筹码放入弃牌堆。游戏在某个玩家筹码用尽时结束。玩家 A、B 和 C 分别起始有 15、14 和 13 个筹码。游戏将进行多少轮？

(A) 36 36

(B) 37 37

(D) 39 39

(E) 40 40

Answer

Correct choice: (B)

正确答案：（B）

Solution

After three rounds the players A, B, and C 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 37th round Player A has no tokens.

三轮后，玩家 A、B 和 C 分别有 14、13 和 12 个筹码。此后每三轮，每个玩家的筹码数减少一个。经过 36 轮后，他们分别有 3、2 和 1 个筹码，第 37 轮后玩家 A 没有筹码了。

Topics