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?

Sorry, I just had a PC moment on my PC.

Let n=4, and let the philosophers be A (white face),B (black face), C (black face) and D (black face). A reasons that B could be laughing at C and D. C could be laughing at B and D. D could be laughing at B and C. A has no proof that his own face is black.

Each of B, C and D see two black faces and one white face.

B reasons that A might be laughing at C and D, C might be laughing at D, and D at C. B has no proof that his own face is black.

C and D reason the same way.

So I think (of course I am wrong) that n must be 2 or 3. Otheriwse n>3 philosphers couldn't conclude that all faces are black. 

Edited on April 13, 2004, 12:28 pm

Posted by Penny on 2004-04-13 12:19:41