Alex, Bert, Carl, Dave, Eddy, Fred, Gary, and Hank have just finished a single elimination contest. They are all knaves, meaning each one alternates between making true and false statements. Each person makes two statements about the contest as follows:

Alex:
1: I played against Carl in the first round.
2: I lost in round 2.

Bert:
1: I played against Dave in the first round.
2: I won the contest.

Carl:
1: I played against Eddy in the first round.
2: I lost in round 1.

Dave:
1: I played against Gary in the first round.
2: I lost in round 2.

Eddy:
1: I played against Fred in the first round.
2: I lost in round 2.

Fred:
1: I played against Hank in the first round.
2: I won the contest.

Gary:
1: I played against Bert in the first round.
2: I lost in round 1.

Hank:
1: I played against Alex in the first round.
2: I lost in round 2.

The contest was setup in a way so that the only way Carl and Dave would play against each other was if they were the final two contestants.

Determine the pairs of players for all seven games in the contest with the given statements.

 Round 1 | Round 2 | Round 3 | Winner

_________
         |_________
_________|         |
                   |_________
_________          |         |
         |_________|         |
_________|                   |
                             |_________
_________                    |
         |_________          |
_________|         |         |
                   |_________|
_________          |
         |_________|
_________|

(In reply to Solution & Explanation by FrankM)

Very interesting!  I am impressed by how you reformulated the problem into boolean logic.

Posted by Brian Smith on 2008-04-07 22:47:56