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?

Call Ernesto E,Fontleroy F,and Gildenstern G.
For any person P and any number N,let PN be P's Nth statement(Example:Fontleroy's second statement is F2).
We notice that for any knight-liar-knave person P and any number N1 and N2 both even or both odd,PN1 and PN2 are either both true or both false(Call this Fact 1).

A knight can never claim to be a knave like Fontleroy did in F1,so F is not a knight.
F can be a knave that told the truth in F1 or a liar who always lies in all his statements.
Either way,F2 and F4 are both false(You can check this).
E is not a knight and G is not a liar.

E said he was a knight and he is not,so E1 is false.
E3 must also be false by Fact 1 at the beginning,so F is not a liar.

Since F is neither a knight nor a liar,he is a knave.

Therefore,G told the truth in G1,and also G3 by Fact 1,so E is a knave.
Since E1 is false and E is a knave,E2 is true,so G is a knight.
We have solved it.

E is a knave,F is a knave,and G is a knight.

P. S. Find all the bold spots.

Posted by Tim Axoy on 2003-05-21 13:37:20