Three young men named Ernesto, Fontleroy, and Gildenstern arrived singly at an inn and awaited the innkeeper. When she arrived at the front desk, all three asked for the best room. The innkeeper explained that, since it was not possible for them all to have the best room, the man who had arrived first could have a spacious room overlooking the village square, the second to arrive could have a small room with a partial view of the garden, and the third would have to settle for a drafty loft by the back alley, but it was the last room she had to offer. The following conversation ensued:

Ernesto: I am a knight.
Fontleroy: While I am only a knave.
Gildenstern: I agree with you there, Fontleroy.
Ernesto: Gildenstern is a knight.
Fontleroy: No, he is a liar.
Gildenstern: Then let me say: I did not arrive first.
Ernesto: Fontleroy is the liar.
Fontleroy: Following Gildenstern's lead, let me say: I did not arrive first.
Gildenstern: Ernesto is a knave.
Ernesto: If that is so, then the most honest of us did not arrive last.
Fontleroy: Ernesto, you are a knight.
Gildenstern: Ha!

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 man, and what room did the innkeeper assign to each?

(In reply to Please Someone Correct Me by Ravi Raja)

The problem is in assuming that each of the three is a different category. If you look at the first two solutions posted you will see that that is proved not to be true, as two are of the same category, which those solutions prove.

Posted by Charlie on 2003-05-18 04:37:17