All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
The three sages (Posted on 2002-05-05) Difficulty: 3 of 5
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?

See The Solution Submitted by levik    
Rating: 3.5455 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Puzzle Solution | Comment 11 of 12 |

Let us denote the sages as A, B and C and in particular, let us assume without loss of generality that the Sage A stopped laughing.
His reasoning is as follows:

If Sage A's forehead is clean then Sage B must be laughing at Sage C whose forehead is dirty. In which case, Sage C would notice that Sage B is laughing and if Sage A's forehead was clean, then Sage B would immediately conclude that his (Sage B's) forehead was dirty, and would stop laughing.
Since, Sage B did not stop laughing, it follows that he must be laughing at Sage A, whose forehead was dirty.
Consequently, Sage A concluded that his forehead was dirty, and  stopped laughing.


  Posted by K Sengupta on 2007-03-12 12:53:49
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information