A man has to win two games in a row in order to win a prize. In total, he has to play only three games. The opponents are weak or strong. He has to at least play one strong opponent, and he cannot play consecutively two weak opponents. What sequence should he choose to play?

For three games, the possibilities of outcome are: loss-loss-loss; loss-loss-win; loss-win-loss; loss-win-win; win-loss-loss; win-loss-win; win-win-loss; and win-win-win.  As can be seen, only the loss-win-win, win-win-loss and win-win-win outcomes result in two consecutive wins. In all cases, the player needs  to win the second game. 

Given a player cannot play against two consecutive weak players, the given combinations for the first two players are: strong-strong, strong-weak, and weak-strong.  Only in one of these combinations is the weak player the second player.  As, by definition, the odds of winning against a weak player is greater than against a strong player, and it is the second game that must be won, the order of the first two players must then be strong-weak.  And again, because there cannot be two consecutive weak players, the third player must also be strong.  Therefore the combination to be played would be strong-weak-strong.

Posted by Dej Mar on 2006-08-01 15:05:47