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?

There are probably many variations on this, but you could point to a route and ask "Will you say "yes" if I ask you if that's the shorter route?"

4 cases:

If it is indeed the shorter route and the Knave tells the truth first, then he will lie to the actaul question and tell the truth about it so  he will say "no".

For the smae route, but with lie-first, he knows we will answer the question truthfully and will therefore lie about it and also say "no".

The other 2 case can be deduced like this, and for this specific question, if you get  a "no", then that is the shorter route, and "yes", then you have pointed to the longer route

Posted by Kenny M on 2009-10-31 19:48:26