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?

1.  "Which path would someone the opposite of you say is the longer path?"  -  The answer to this question will reveal the shorter path.

2.  "If I were to ask you with my next question which path is the longer one, what would your answer then be?"  -  The answer to this question will reveal the shorter path.

3.  "Which path would a Liar say is the longer path?"  -  The answer to this question will reveal the shorter path.

Really, only one question is needed.

Posted by hoodat on 2011-02-14 16:01:12