2008 09 30
Liar Liar


Posted by in: logic, Philosophy, puzzles

Leiter tells me that you can win a book. If you answer this question correctly, your name goes into a drawing.

A logician vacationing in the South Seas finds himself on an island inhabited by the two proverbial tribes of liars and truth-tellers. Members of one tribe always tell the truth; members of the other always lie.

He comes to a fork in a road and has to ask a native bystander which branch he should take to reach a village. He has no way of telling whether the native is a truth-teller or liar. The logician thinks a moment and then asks one question only. From the reply, he knows which road to take.

What question does he ask?

…For our purposes here, we’ll assume that the answer is confined to a single “yes” or “no.”

I had heard this one years ago, and cannot now remember if I figured it out on my own or not. (Probably not, knowing my limitations.)  The only snag is that either I’m wrong, or else the last instruction—”the answer is confined to a single “yes” or “no.””—is slightly misleading. Here’s a hint: the instruction is playing fast and loose with the use/mention distinction. Oh, and if my solution works, then there are actually two questions he could ask.

Anyway, I submitted an answer.  We’ll see what happens.


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