Here’s a fairly recent twist on an old type of logic puzzle. A logician vacationing in the South Pacific finds himself on an island inhabited by the two proverbial groups of liars and truth-tellers. Members of one group always tell the truth, while members of the other always lie. He comes to a fork in a road and has to ask a bystander which branch he should take to reach a village. He has no way of telling whether the bystander is a truth-teller or a liar. The logician thinks a moment, then asks one question only. From the reply he knows which road to take. What question does he ask?
The logician points to one of the roads and asks, “If I were to ask you if this road leads to the village, would you say ‘yes’?” The bystander is forced to give the right answer, even if he is a liar! If the road does lead to the village, the liar would say “no” to the direct question, but as the question is put, he lies and says he would respond “yes.” Thus the logician can be certain that the road does lead to the village, whether the respondent is a truth-teller or a liar. On the other hand, if the road actually does not go to the village, the liar is forced in the same way to reply “no” to the inquirer’s question. More complicated forms of the question to the bystander can be devised, but they all hinge on the same logical principle: namely, that a double negative is equivalent to an affirmative.
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A version of this puzzle originally appeared in the February 1957 issue of Scientific American.