3

I'm working on the following riddle that I found to be kind of interesting, but I can't figure it out. The problem is as follows:

A prince visits an island inhabited by two tribes. Members of one tribe always tell the truth, and members of the other tribe always lie.

The prince comes to a fork in the road. He needs to know which road leads to the castle so as to avoid the fire-breathing dragon and rescue the princess from the wizard holding her captive in the castle.

Standing at this fork in the road is a member of a tribe who has time to answer only one yes or no question, but the prince can't tell which tribe he belongs to. What question should he ask to find the road to the castle?

Is there a way to solve this problem without involving another member of a tribe. I believe there is an easy solution to this problem if you have more than one member of a tribe to ask, but can this be solved if you only have one member to ask?

Community
  • 1
Amateur Math Guy
  • 1,411
  • See my answer to similar question at: http://math.stackexchange.com/questions/179968/what-is-the-name-of-the-logical-puzzle-where-one-always-lies-and-another-always/184907#184907 – Dan Christensen Feb 04 '13 at 06:26

1 Answers1

4

Point along one of the two roads and ask: ‘If I were to ask you whether this is the road to the castle, would you say yes?’

If you work out the possibilities, you’ll see that the indicated road is the road to the castle if and only if the speaker says yes. For instance, suppose that it’s the right road, and the speaker is a liar. Then his answer to the question ‘Is this the road to the castle?’ would be no, since he lies; but being a liar, he lies about his answer and says yes to the actual question.

Brian M. Scott
  • 616,228