A Baron, a Count, a Duke and an Earl met at a jousting tournament. In the first round, two met in the first joust, and the other two met in the second joust; the two winners from the first round met at the second round for the final joust. After the jousting, they declared:

Baron: I beat the Earl.

Count: I faced both the Baron and the Duke.

Duke: I didn't make it past the first round.

Earl: At the first round, I lost to the Duke.

I knew how many were knights, and how many were liars (though not who was what) but that wasn't enough to know what jousts there had been.

However, I happened to know that a certain joust had taken place (though I didn't know who won and if it had been in the first or the second round) and that allowed me to know every result.

Can you deduce this?

(In reply to re(2): Ignorance is key - help! by Paul)

Thanks Paul, I feel better about not seeing this. I would think this reasoning belongs in any general argument.

What throws me is that we are able to conclude who are the knights and liars AND the baron faces the earl and beats him in the second round. All of this comes only from the fact that the author can describe the whole tournament from knowing one paring.

What is twisting for me is that the author knows the number of knights, but he can't have derived this as you have, as he didn't know that he would be able to derive who wins until after he is told a pairing. Thus this knowledge came from outside, but is ultimately a red herring for us. All we needed to know was his ability to solve the whole thing upon knowing a single pairing. Agree?

Posted by owl on 2005-08-16 13:59:48