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).

Since the judge was not a knave and he contradicted himself, he must be a liar, so neither Bert nor Coby won.

Coby's first statement was that a certain person (Dave) won, so his second statement would also have to be about stating a certain person won. Only statements a, b and e do this. Coby couldn't have made statement a as then he'd be agreeing with himself, which is not allowed for a knave. That leaves b and e. Either one would be a lie as neither he (Coby) nor Bert won. Thus his first statement (Dave won) would have to be true.

Therefore Dave won.

Posted by Charlie on 2003-08-02 05:17:49