¶ 2007-03-06 21:43:00 +0000
Today I set my Google Talk status to the following riddle:
You reach a fork in a path. One way leads to a village of nice people who always tell the truth. The other leads to a village of mean cannibals who always lie. A representative from each village is at the fork, but you donʼt know who is who. You can only ask one question, and both representatives will answer the question. Based on the answers you receive you must choose one of the paths to walk down. What is your question?
The first person to find a correct solution was my sister Lorraine. The question she asked was, “If I asked the other person which way the truth-telling village is, what would his answer be?” Both representatives pointed to the same path, and Lorraine ran the other way.
Now, thatʼs a complicated question. For anyone who was as confused as I was, here is the explanation:
We will call the solution the “outer question,” because it contains a hypothetical “inner question.”
If the liar was asked the inner question, he would point to his own village, the one full of cannibals who lie. Therefore, when the truth-teller is asked the outer question, he will point to the lying village.
If the truth-teller was asked the inner question, he would point to his own village, the one full of nice people who wouldnʼt eat you. Therefore, when the liar is asked the outer question, he will point to the lying village.
So there you are, standing at a fork in the road with two people pointing the way to the village of liars, and you decide to run the other way. Good choice.
This solution works, but it isnʼt what I was thinking of. There is a simpler answer. Or rather, there is a simpler question.
I asked, “Which way is it to your village?” Then I ran the way they pointed.
When Lorraine asked me why you have to run, I answered, “Because you are being chased by a bear.”