While traveling, you come upon a fork in the road. One path is the short route to your destination, the other is the long 'scenic' route. You do not know which route is which, but a man at the intersection does.

(Case 1) He is either a knight (always tells the truth) or a liar (always lies). By asking him one question, can you determine which route is the short route?

(Case 2) He is a knave (strictly alternating true and false statements), but you do not know if his next statement will be true. By asking him one question, can you determine which route is the short route?
How does this differ from case 1?

(Case 3) He could be a knight, a knave, or a liar. With two questions, can you determine which route is shorter?
Is it possible to determine which route is shorter with one question?

Case1) If my next question was asking you to point out the shorter route, which would you show me?

Liars and Knights shall point to the shorter route.

Case2) If my next question was asking you to point out the shorter route, which would you show me?

Knaves shall always point to the longer route.

Case3) If my next question was asking you to point out the shorter route, which would you show me?

Was your last statement a lie?

For second question, if they answer no then he is either a liar or knight and if they answer yes then he is a knave.  Remember the response to the initial question and refer to Case1 or Case2.

Case3 BONUS) If my question after my next question is to point out the shorter route, where would you show me?

Everybody shall point to the shorter route!!!

Posted by Andre on 2010-05-24 18:05:03