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 stableboys 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?
This was a nice problem and very easy to work out. I simply made the True/False list that follows then tested A for each of the personalities. Attached is the final solution that I worked out. (Caps are the correct answers)
A. t/F - Liar
B. T/f t/F
C. T/f T/f
A. t/F t/F - Liar
C. T/f
B. T/f
A. Ajax is the Lair
B. Balthzar is the Knave
C. Cicero is the Knight
From there we know that Balthzar did not arrive second as statement 5 and 6 show and since Cicero was telling the truth in statement 3 that he came first then Balthzar came in last and the puts Ajax in second place.
Cicero - Spare bunk
Ajax - Stable
Balthzar - pighouse
Yes, this may be some screwed up logic, but it works for me...
Deduction
