Mr. and Mrs. Anderson and Mr. and Mrs. Barton competed in a chess tournament. Of the three games played:

(i) In only the first game were the two players married to each other.

(ii) The men won two games and the women won one game.

(iii) The Andersons won more games than the Bartons.

(iv) Anyone who lost a game did not play the subsequent game.

Who did not lose a game?

I expected Mr. Anderson to win just by considering (ii) and (iii) but that's not how it turned out...

(i) rules out a bracket tournament since once a couple plays against each other the other one cannot.  Therefore the winner of the first match must then play against each of the other two people.

Game 1 is either Mr. A vs Mrs. A or Mr. B vs Mrs. B
we can consider each winner as one of the four cases.

Case 1 Mr. A wins.
He needs a second win (iii) so he has to win his second match.  So he can't play Mrs. B or the women will have no wins which is counter to (ii).  So he beats Mr. B and then in the third game, Mrs. B beats him.  Mrs. B did not lose a game.

Case 2 Mrs. A wins.
She cannot win again (ii) but if she loses then the last game will be the other couple which is counter to (i) and also counter to (iii).
Not possible.

Case 3.  Mr. B wins.
He cannot win again (iii) but if he loses  then the last game will be the other couple which is counter to (i).
Not Possible.

Case 4. Mrs. B wins.
She cannot win again (ii) and (iii) but if she loses then the last game will be the other couple which is counter to (i).
Not possible.

Posted by Jer on 2012-02-03 11:02:56