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?
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
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.