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 Solution by Trevor Leitch)

Using Trevor Leitch's statement numbering system of E1 - F4:

By F1, F is not a knight by the same reasoning Trevor used.

Then F2 is false, as F is either a knave who previously spoke the truth and is now lying or is a liar who is continuing to lie, so G is not a liar.

Since F2 is false, so is F4, so E is not a knight.

So E1 is false, and therefore also E3, so F is not a liar.

Since F is not a liar nor a knight he is a knave, so F1 is true and therefore also F3, so F did not arrive first.

As G1 agrees with true statement F1, it is also true, making G3 also true, so E is a knave.

Since E is a knave and E1 is false, E2 is true, so G is a knight.

Since G is a knight, G2 is true, and G did not arrive first.

Since F did not arrive first and G did not arrive first, E must have arrived first.

Since E2 is true E4 is true and the most honest (G, the only knight) did not arrive last. Since G did not arrive first, he arrived second.

Since E arrived first, getting the best room; G arrived second, getting second best; F arrived last, getting the worst.
And to recap, E and F are knaves and G is a knight.

Posted by Charlie on 2003-05-16 05:44:59