The Lying, Confused Natives: Answer

Are you sure you want to read the answer? Maybe you should go back and ponder the Lying, Confused Natives puzzle a bit longer. Once you read the answer, you can't un-read it! It's a tough logic puzzle so don't feel bad if you can't think of an answer right away. Send an email to me at mazes if you have questions!

The Answer...

By asking the following question Jones can be assured of survival:

"If I were to ask a member of the tribe to which you do not belong if the left path leads to safety for me, would he say Ug?"

When Jones is pointing to the correct path, the elder will always answer Ug."

This question works because by asking the elder to answer for a member of the tribe to which he does not belong, both the uncertainty in whether he is telling the truth and the uncertainty in whether he is disoriented is eliminated. If the elder is a liar, a member of the other tribe is telling the truth, and visa-versa, so taken together this will always lead to an incorrect answer. Similarly, if the elder is disoriented, then the other tribesman is not (and visa-versa), so taken together this too will always lead to an incorrect answer. The combined effect of two incorrect answers is a correct answer (since there are only two paths), so we are left only with the uncertainty in the language, which is dealt with by the phrase "would he say Ug?"

Since we do not have to worry about liars and disoriented smokers, who cancel each other out, we can consider both tribesman to be truthful in terms of the language issue. For example, imagine a situation where the left path is the incorrect path and 'Ug' = 'no'. Jones is then pointing to the incorrect path and asking the elder "If I were to ask a member of the other tribe if this path leads to safety, would he say no?" The elder would say 'yes' (or 'Um'), for the other tribesman would indeed say that it was not the safe path. Similarly, if 'Ug'='yes' the elder would answer 'no,' which is still 'Um.' So as long as Jones is pointing to the incorrect path, the elder will answer 'Um.' Similarly, when Jones is pointing to the correct path, the elder will always answer 'Ug.'

Thus, if the elder answers 'Ug' to Jones's question, the left path is the safe path; if he answers 'Um' the left path is not safe. Either way Jones can now escape to freedom!

For the skeptical, the brute force method of testing this question with a binary tree of all possible situations also works (path=safe or not safe; elder=truth-teller or liar; elder=smoker or nonsmoker; Ug=yes or no). There are only 16 possible situations, but it takes some concentrated effort to think each one through without getting confused!

I hope you enjoyed this mind-bending puzzle!

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The Lying, Confused Natives: Answer

The Answer...

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