A logician has a favorite game to play at parties. He shows a set of solidly colored stickers to all his logician friends. Each logician, without looking, puts a random sticker on his/her own back. Each logician can only see the stickers on other people's backs, and no one can look at the unused stickers. The logicians take turns announcing whether they can deduce their own color. The game ends when someone announces he/she can deduce his/her own color.

One time while playing this game, no one had yet ended the game even though everyone had a turn. Should they continue to take second turns, or should they just give up and start a new game? Prove that it is impossible for a game that hasn't ended after everyone's first turn to ever end, or provide a counterexample.

(In reply to re(2): armando by armando)

I think I understand what you are saying.  But I believe this game can get more complicated than you think.  When the logicians deduce their own color, they may be using the "silence" of more than one other logician.  Take the following example:

5 logicians, 4 red stickers, 3 blue stickers.
Imagine the first three logicians get blue, while the other two get red.  The first two logicians will fail to guess, but the third will win.  The third wins because of the the both of the previous logician's failures to guess.  If either of the previous logicians had missed his turn, the the third would not be able to correctly guess.

Posted by Tristan on 2005-03-22 23:57:47