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 went through different options systamatically but once i found one i think works i havent checked other options so there may be others:
Having Ajax telling the truth would not work no matter who of the others was a liar or a knave.

i then tried with Ajax being the liar, Balthazar beind a knight and Cicero the knave...this worked and the order of people i got is Balthazar, Ajax and then Cicero so:
Balthazar: spare bunk
Ajax: stable
Cicero: pighouse

Posted by sarah on 2003-06-26 07:14:45