Three young men named Ajax, Balthazar, and Cicero arrived singly at an inn and awaited the innkeeper. When she arrived at the front desk, the innkeeper explained that no rooms were available, but as the rains were especially harsh that season she was willing to put up the three men as best she could. The man who arrived first could sleep in a spare bunk in the stableboy’s room, the second to arrive could sleep in the stable, and the third would have to bunk in the pighouse, which at least was warm and dry. The following argument ensued:

Ajax: I arrived first.
Balthazar: No you didn't! I was first.
Cicero: You were not! I arrived first.
Ajax: That's a lie! I arrived first, as I said before.
Cicero: Well, Balthazar did not arrive second.
Balthzar: Agreed.

The innkeeper knew that everyone in these parts was either a knight who always told the truth, a liar who never told the truth, or a knave whose statements strictly alternated between truth and untruth. Using deductive reasoning, what is the disposition of each young man, and what berth did the innkeeper assign to each?

I haven't finished solving this yet, but my first observation is that all the statements but one refer to who is first.

Cicero's second statement, "Balthazar did not arrive second," must be true or false.
If it's false, then B is second, the other clues will determine who was first, and we know who was third by elimination.

If that statement is true, B can be first or third. If it means B is first, however, there are no other clues that will help us determine who is second or third in what order.
Therefore, in order to be able to solve the problem, the truth of that statement must imply that B is third.

Either way, I think that in order to have a concrete solution, B cannot be first, or we will not know which of the other two came earlier.

Posted by DJ on 2003-06-25 10:31:38