阿拉伯苏丹
Arabian Sultan
题目详情
从前，一位阿拉伯苏丹俘虏了 50 名智者，并将他们关在不同的房间里。每隔一分钟，苏丹就会叫一名囚犯到他的房间，他面前的桌子上会放一个玻璃杯。智者可以选择把杯子翻过来或者什么也不做。
智者被释放的唯一方法是他们中的一个人正确地陈述他们都至少被召唤到苏丹一次。如果这个说法有误，所有智者都会被处决。在智者被囚禁在不同的房间之前，他们只被允许交流一次。
是否存在一种策略可供智者使用，以确保每个人在发表声明之前都至少被苏丹召唤过一次？
Once upon a time, an Arabian sultan captured 50 wise men and kept them in separate rooms. Every minute, the sultan would call one prisoner into his room where he would have a glass rested on the table in front of him. The wise men could choose to turn the glass over or do nothing.
The only way for the wise men to be released was if one of them correctly stated that they have all been called to the sultan at least once. If the statement was wrong, every wise man would be executed. Before the wise men were imprisoned in separate rooms, they were allowed to communicate only once.
Does there exist a strategy that the wise men can use to ensure that everyone has been called by the sultan at least once before making the statement?
解析
策略如下。智者会从50人中指定一名发言人（发表声明的人），其余49人对称行事。该策略包括让 49 位智者在第一次看到玻璃面朝上时将其翻转过来。每次看到玻璃面朝下时，发言人都会将玻璃面朝上翻转。第 49 次翻转后，发言人可以宣布所有智者都已被召集。
Original Explanation
The strategy would be as follows. The wise men would designate one spokesman (the person to make the statement) out of the 50 men, and the remaining 49 men would act symmetrically. The strategy would involve having each of the 49 wise men flip the glass upside down the first time they see it facing up. The spokesman would flip the glass facing up each time he sees it facing down. After the 49th flip, the spokesman can declare that all wise men have been called.