In this problem, only the original light is necessary. The rest are just a kind signals to tell them try again. They could be bell rings or whistles. Let's change the question a little:
一群人开舞会，每人头上都戴着一顶帽子。帽子只有黑白两种，黑的至少有一顶。每个人都能看到其他人帽子的颜色，却看不到自己的。主持人先让大家看看别人头上戴的是什么帽子，然后关灯，如果有人认为自己戴的是黑帽子，就打自己一个耳光。第一次关灯，有打耳光的声音响起。问有多少人戴着黑帽子？
The common answer is 1. But 2 is also possible. So are 3, 4,... . The more reasonable answer should be: If the slap sounds right away after the room is dark, one person has black hat. If the slap sounds after a while, then two people have black hat, and so on. If you do not believe this, you can ask a few people to try.
一群人开舞会，每人头上都戴着一顶帽子。帽子只有黑白两种，黑的至少有一顶。每个人都能看到其他人帽子的颜色，却看不到自己的。主持人先让大家看看别人头上戴的是什么帽子，然后关灯，如果有人认为自己戴的是黑帽子，就打自己一个耳光。第一次关灯，有打耳光的声音响起。问有多少人戴着黑帽子？
The common answer is 1. But 2 is also possible. So are 3, 4,... . The more reasonable answer should be: If the slap sounds right away after the room is dark, one person has black hat. If the slap sounds after a while, then two people have black hat, and so on. If you do not believe this, you can ask a few people to try.
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