MOU got it in one.
Three players enter a room and a red or blue hat is placed on each person's head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players' hats but not his own.
No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a hypothetical $3 million prize if at least one player guesses correctly and no players guess incorrectly.
The same game can be played with any number of players. The general problem is to find a strategy for the group that maximizes its chances of winning the prize.
One obvious strategy for the players, for instance, would be for one player to always guess "red" while the other players pass. This would give the group a 50 percent chance of winning the prize.
Question: Can the group do better than 50%
Four men and four women are shipwrecked on a deserted island. Eventually each person falls in love with one person and is loved by one person. You are given the following information:
o Chad loves the girl who is in love with David.
o Arthur loves the girl who loves the man who loves Ellen.
o Bruce loves the girl who loves the man who loves Mary.
o Gloria does not love Bruce.
o Helen loves a man who does not love Gloria.
o There is no mutual love interest (nobody loves the person who loves them back)
o Nobody is homosexual or narcissist.
Who loves who