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?

if there are n "equally brights" philosophers , each one started laughing at the other, each philosopher see (n-1)philosophers with the faces painted in black, and see (n-1) philosophers laughing, but because "all" of them are laughing, all of them see n-1 philosophers with black faces, and that mean that all have the faces painted in black, i think that n*(n-1)/n-1=n(all of them) .

Posted by JCD on 2004-04-14 20:22:51