Question

一个游戏按如下规则使用筹码：每轮中，筹码最多的玩家给其他每位玩家各一枚筹码，并且再把一枚筹码放入弃置堆。当某位玩家筹码用完时游戏结束。玩家 $A$ 、 $B$ 、 $C$ 分别以 $15$ 、 $14$ 、 $13$ 枚筹码开始。游戏会进行多少轮？

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?

$36$

$37$

$38$

$39$

$40$

答案：B

知识点：过程模拟找规律

难度评级：1390

解答：

前三轮后，筹码数从 $(15, 14, 13)$ 变为 $(14, 13, 12)$ 。

一般地，每三轮后每位玩家都减少一枚筹码。 $36$ 轮后筹码数为 $(3, 2, 1)$ 。第 $37$ 轮中，领先者给出三枚筹码后降到 $0$ ，游戏结束。

所以正确答案是 B。

After the first three rounds the counts go from $(15, 14, 13)$ to $(14, 13, 12).$ In general, every three rounds each player loses exactly one token.

After $36$ rounds the counts are $(3, 2, 1).$ On the $37$ th round the leader gives away three tokens and drops to $0,$ ending the game.

Thus, the correct answer is B.

2004 AMC 10A 第 8 题

答案：B

难度评级：1390

解答：

其他年份的第 8 题