1,000 mathematicians live on an island. 600 have brown eyes, and 400 have
blue eyes. According to an ancient tradition which is honored by all, if a
personever discovers that they have blue eyes, they will promptly commit
suicide the following morning.
There are no mirrors on the island, and it is considered to be in very
poor taste to discuss the subject of eye color. Of course, everyone
knows what everyone *else's* eye color is.
One day, a soothsayer passes through the island, and in the presence of
the assembled inhabitants solemnly announces: "At least one of you on
this island has blue eyes."
1) What happens?
2) What information was divulged by the soothsayer that wasn't
common knowledge before?
3) extra credit: suppose each of the blue-eyed inhabitants had resolved
not to commit suicide if they ever discovered their eye color. what
happens now? (submitted by Steven Phelps)