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The many sages (Posted on 2004-04-13) Difficulty: 3 of 5
This is a generalisation of "The three sages"

On a hot summer day, n equally bright philosophers, tired from all that philosophising, were napping in an orchard. A prankster came by, and painted all of their faces black with charcoal.

When the philosophers woke up, they started laughing at the others... until they suddenly realised all of their faces must be black!

How did they come to that conclusion?

See The Solution Submitted by e.g.    
Rating: 2.3636 (11 votes)

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Many Sages | Comment 9 of 24 |
Lets assume that there are four sages and all four know about "the three sages".  After some time had passed, they would all realize that if their own face was clean that one of the other three would have stopped after realizing he was in the "three sages" scenario.  But since no one has stopped yet, then all four of them must have their faces painted.

If there are n sages who all know about the n-1 scenario, then after some lengthy period of time, they would eventually realize that they are in an n sages scenario and not a n-1 scenario.

  Posted by Brian Smith on 2004-04-13 14:05:04
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