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 re(2): Please Someone Correct Me by Ravi Raja)

You say
But have you gone through my proof Charlie? Just see what conclusion I am arriving at. Ernesto does not belong to any of the three categories (Knights, Knaves or Liars). How is that possible? That was what I wanted others to correct and not whether they belong to same or different categories.

But it is not necessary to go through the proof. If one starts with contradictory premises, one can prove anything. The contradictory premises in this case are 1) All the people are different types and 2) The clues that are given, which contradict this. In fact, you have proved that they are not all different types because by starting with that assumption, you have come up with the impossibility that Ernesto is not any of the types.

It is always possible to prove an impossibility by starting out with contradictory premises. Again, looking at it the other way around, if an impossibility has been proved, one has demonstrated that at least one of the premises is wrong.

Posted by Charlie on 2003-05-20 11:06:33