An annual knave (someone who alternates between truth and lie) race was held in Knavesville. There was one judge, who was either a knight or a liar, and all of the racers were knaves. After the race a news team asked the top five finishers and the judge who won. These were their answers:

Alex - I won.
Bert - Alex won.
Coby - Dave won.
Dave - I came 3rd.
Ed - I won.
Judge - Bert won.

Confused, they asked them all again, but their names all got lost, so the order is muddled up.

Runner a - Dave won.
Runner b - I won.
Runner c - I didn't win.
Runner d - I came 4th.
Runner e - Bert won.
Judge - Coby won.

Can you work out who won? (Assuming each individual's comments were similar, i.e. both of their comments would suggest that a certain person won, or their own position).

So far there is a solution that Dave won, but assume the racers finish A, B, D, E, and C, and that each made the following second statement:

Alex: Dave won.
Bert: I won.
Coby: I didn't win.
Dave: Bert won.
Ed: I came 4th.

In this scenario, each person makes one true statement and one false statement. Therefore, A could also be the winner, given the statements.

Posted by Bryan on 2003-08-02 13:53:44