perplexus.info :: Liars and Knights : Unknown answers

Unknown answers (Posted on 2003-05-13)

Timothy once visited a land of knights and liars,and met two inhabitants,A and B. He had the following conversation.

Timothy:A,is B a liar?
Timothy hears A's answer,but he will not tell you what it was.
Timothy:B,are you both liars?
Timothy hears B's answer,but he will not tell you what it was.
At this point,I will not tell you whether or not he knew what they were.

He once told his friend what questions he asked,but not what answers he got. The friend did not have enough information,so the following dialogue occurred.

Friend:Were your answers the same?
Timothy's friend hears his answer,and finally the friend has enough information to solve what A and B are.
What are they?

Submitted by Tim Axoy

Rating: 4.0000 (7 votes)

Solution: (Hide)

We make a chart of what answers A and B would give(K means knight,L means liar).
1:A-K,B-K,A says no,B says no.
2:A-K,B-L,A says yes,B says yes.
3:A-L,B-K,A says yes,B says no.
4:A-L,B-L,A says no,B says no.

We see that the 3 is the only case in which the answers are different. Now,if Timothy said yes to his friend's question,the friend would have just eliminated 3,but would not be able to solve it. Therefore,Timothy said no and 3 holds;A is a liar and B is a knight.

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

Subject	Author	Date
Answer	Math Man	2012-05-09 17:02:55
Nice Puzzle	K Sengupta	2007-03-04 04:30:53
solution	FatBoy	2003-08-13 11:04:20
re(2): Solution	Hank	2003-05-14 03:35:13
Charlie did it!!	Tim Axoy	2003-05-13 13:11:07
Both wrong answers	Tim Axoy	2003-05-13 13:08:18
Liar's Knight at the Knight's Lair	Sanjay	2003-05-13 12:27:45
Liars have to be True to themselves	Sanjay	2003-05-13 11:56:07
re: Solution	Sanjay	2003-05-13 11:33:36
re: Solution	Charlie	2003-05-13 04:30:43
solution	Charlie	2003-05-13 04:21:29
Solution	Ravi Raja	2003-05-13 04:19:26
Solution	Hank	2003-05-13 03:08:27

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