perplexus.info :: Liars and Knights : One Native, Two Roads

One Native, Two Roads (Posted on 2006-05-22)

You are lost once again in the land of Knights, Knaves, and Liars, and once again you find yourself at a fork in the road. You know that one path will lead you to a safe return home, while the other will lead you to your own gruesome demise. (You really need to find a better vacation spot next year!)

Standing at the fork is a native, who might be either a Knight (who always tells the truth), a Knave (who alternates between true and false statements), or a Liar (who always lies). You have no way of knowing which he is. Worse yet, you realize that if he is a knave, you don't know if he will tell you the truth first, and then lie, or lie first and then tell the truth, etc.

What is the fewest number of questions you have to ask to find out which is the safe road, and what are they?

Submitted by tomarken

Rating: 3.8333 (6 votes)

Solution: (Hide)

One possible solution uses two questions:

1. "Are you a knave?"

A Knight would say no.
A Lie-first knave would lie and say no.
A Truth-first knave would tell the truth and say yes.
A liar would say yes.

Therefore, if the native says "no" to question #1, you know that they are either a Knight or a Lie-first knave. Either way you know that they will tell the truth on the next question.

Similarly, if the native says "yes" to question #1, you know that they are either a Liar or a Truth-first knave. Either way you know that they will lie on the next question.

Once you know this, you ask the second question:

2. "Is this the safe road?"

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

Subject	Author	Date
ONE QUESTION	Andre	2010-05-28 18:58:30
answer	K Sengupta	2007-05-09 13:27:02
re: 3 to 5 questions, depending on who you figure out first	liz	2006-06-09 09:48:16
3 to 5 questions, depending on who you figure out first	liz	2006-06-09 09:27:09
3 Questions	Dax Fuiten	2006-05-29 00:11:03
Just a guess	Salil	2006-05-28 01:56:58
The safe road	Gina Ernyey	2006-05-26 14:15:54
re(4): The jury isn't in. (re: question and solution)	Dej Mar	2006-05-25 01:56:54
re(3): The jury isn't in. (re: question and solution)	Venkat	2006-05-25 00:34:35
re(2): The jury isn't in. (re: question and solution)	Dej Mar	2006-05-25 00:28:03
re: The jury isn't in. (re: question and solution)	Venkat	2006-05-24 23:44:13
The jury isn't in. (re: question and solution)	Dej Mar	2006-05-24 08:26:24
re: My solution	Vernon Lewis	2006-05-23 07:17:33
single question	Robby Goetschalckx	2006-05-23 03:36:33
My solution	Caleb	2006-05-23 02:59:55
answer	Rachael	2006-05-23 02:05:08
re: What I would do	Josh	2006-05-23 01:25:18
Home Sweet Home	Dej Mar	2006-05-23 00:57:41
re: What I would do	MathManiac	2006-05-22 23:18:28
What I would do	Vernon Lewis	2006-05-22 17:09:17
2 questions	Patrick	2006-05-22 15:18:09

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