Mr. and Mrs. Anderson and Mr. and Mrs. Barton competed in a chess tournament. Of the three games played:
(i) In only the first game were the two players married to each other.
(ii) The men won two games and the women won one game.
(iii) The Andersons won more games than the Bartons.
(iv) Anyone who lost a game did not play the subsequent game.
Who did not lose a game?
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?
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