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?

Ask him "If I asked you, which way would you say is the short route?"

A Knight will answer by indicating the short route

A Liar, if asked the question "which way is the short route", would indicate the long route, but since he will lie about his answer, he will indicate the short route based on the question above

I need more time to think about parts 2 & 3

Posted by Kenny M on 2009-10-31 16:38:40