perplexus.info :: Liars and Knights : The Best Room at the Inn

The Best Room at the Inn (Posted on 2003-05-16)

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?

Submitted by Bryan

Rating: 3.8571 (7 votes)

Solution: (Hide)

Call the men E, F, and G, and number the statements 1 through 12.
If F is a liar, 11 is false, making E a liar or knave. If so, 1 is false, and in either case 7 is also false, so F cannot be a liar. If F is a knight, 11 is true, making E a knight. If so, 7 is true and F is a liar, so F cannot be a knight. Thus F is a knave.
Therefore 2 is true, so 3 is also true and G is either a knave or a knight. In either case, 9 is true, making E a knave.
Therefore 1 is false, making 4 true, and G is a knight.
6 is true. Since 2 is true, 8 is true, and since 4 is true, 10 is true. G did not arrive first (6) or last (10), so he arrived second. F also did not arrive first (8), so E was first and F was last.
Ernesto got the spacious room overlooking the town square,
Gildenstern got the small room by the garden, and
Fontleroy was stuck with the loft.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2022-09-02 00:42:53
Sol	Andre	2010-06-04 17:58:46
Find the bold spots.	Tim Axoy	2003-05-21 13:37:20
re(4): Please Someone Correct Me	Ravi Raja	2003-05-21 04:52:16
re(3): Please Someone Correct Me	Bryan	2003-05-20 18:51:24
re(3): Please Someone Correct Me	Charlie	2003-05-20 11:06:33
re(2): Please Someone Correct Me	Ravi Raja	2003-05-20 09:44:16
re: Please Someone Correct Me	Bryan	2003-05-20 06:35:21
re: K&L&K	Ravi Raja	2003-05-20 01:30:43
re(2): Please Someone Correct Me	Ravi Raja	2003-05-20 01:28:27
Correction!	Silly Jilly	2003-05-18 07:40:12
re: Please Someone Correct Me	Jackie	2003-05-18 07:25:46
K&L&K	Tim Axoy	2003-05-18 06:22:48
re: Flocking Together	Charlie	2003-05-18 04:38:27
re: Please Someone Correct Me	Charlie	2003-05-18 04:37:17
Flocking Together	Sanjay	2003-05-18 01:34:47
Please Someone Correct Me	Ravi Raja	2003-05-17 19:37:39
Same answer--different sequence of logic	Charlie	2003-05-16 05:44:59
re: Solution	Trevor Leitch	2003-05-16 04:52:39
Solution	Trevor Leitch	2003-05-16 04:47:28

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