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.

You are looking for games that last more than one round but will eventually end, or are looking for a proof that there are none.

The set of stickers can be anything. For example, red, red, blue, white, green, green. If there were 3 logicians, they each don't see their sticker, but do see the two stickers of the other two logicians, and nobody sees the other three stickers.

What you can't count as games that can end after turn 1 are games that can't end, and games that end on turn one. For example, if there were 3 logicians, and 3 red stickers and 3 blue stickers, then the game would never end. If there was 3 logicians and 1 red, 1 blue, and 1 green sticker, then the game would end on turn 1.

Posted by Gamer on 2005-03-18 19:48:53