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?

(In reply to re(4): i think... by DJ)

It depends upon your definition of a statement, but I considered it to be unsolveable.  A statement differs from a sentence, and therefore many statements can be made in a single sentence.  For instance, I could say, "The butler arrived first, followed by the maid, followed by the cook."  There are three statements made in that sentence. 

If we assume that each sentence is a single statement, then a Knave could make as many true comments in a row as he wanted, as long as it were still the same sentence.  In addition, if it is considered one statement - then how do you classify which part of the entire statement makes it true or false.  In this statement "I arrived first, as I said before." - half would be true, half would be false.  Does the statement become false because the first half of the statement is false?  Would it then be true had he said "As I said before, I arrived first" ?

Obviously Ajax did say "I arrived first" before, making that a true statement.  Unfotunately nothing else works out if it is considered that way - so that can't be correct.

Anyway - my thoughts.

Posted by Telly on 2004-06-09 15:42:14