perplexus.info :: Logic : The three sages

The three sages (Posted on 2002-05-05)

On a hot summer day, tired by long discussions, three wise sages were slumbering inthe shade of a tree. A prankster was walking by, and couldn't pass up such an opportunity. He took a piece of charcoal, and put a black spot in the middle of each sage's forhead, careful not to wake them.

When the men did wake, they looked at each other, saw the black marks and began laughing. Each one thought that his two friends had the mark, while his own forhead was clean.

Suddenly, one of them stopped laughing, having realized that his forhead must be dirty as well. How did he arrive at this conclusion?

Submitted by levik

Rating: 3.5455 (11 votes)

Solution: (Hide)

The sages were initially laughing as they all thought that the other two were the only ones with the dirty forehead. The fact that the other two were also laughing didn't alarm them, as they could be laughing at one another.
Then one sage thought: "If my forehead is clean, then the second sage is laughing at the third one. But then the third one would see that the second one is laughing, and if my forehead was clean would undestand that the second sage is laughing at him. He would then realize that his forehead is dirty, and stop laughing. The fact that he doesn't, means that he thinks the second sage is not laughing at him, but rather laughing at me. That means he sees that my forehead is dirty. I better stop laughing."

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Answer	Math Man	2013-08-31 20:43:50
Puzzle Solution	K Sengupta	2007-03-12 12:53:49
re: old problem new phrasing	Amon	2005-04-30 01:55:21
re: this is the solution	Danny	2004-04-14 16:42:23
old problem new phrasing	Ariel	2004-02-28 23:56:12
Solution	Gautam Joshi	2002-12-03 00:06:06
how is that funny	Mike	2002-05-10 15:20:46
this is what happened	theBal	2002-05-07 07:55:32
What about the Prankster?	Paul	2002-05-07 06:59:33
this is the solution	theBal	2002-05-06 17:48:29
Solution	MysticGreenWolf	2002-05-06 09:04:13
Hi	shelli	2002-05-05 18:45:22

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