Mostly Harmless

The best of the Two Tribes problems - Part 1

We were on holiday in a hut in a remote spot in Devon when I was eleven or twelve years old. On sunny days we walked down to the beach (about two miles away) and played all day, returning at night with as much driftwood as we could carry. On rainy days we burnt the driftwood on the hut's hearth which was backed by a fat black pipe thrown into folds like the body of a prone python. The water heated in the pipe rose by convection to a half-buried tank some way up the hill behind the hut.

Most of a rainy day was spent indoors reading books from the hut's ample stock of paperbacks and it may have been there that we discovered the first collection of Mathematical Games made from Martin Gardner's long-running column in Scientific American and published by Pelican - or we might have brought it with us. At any rate, it was there that we read his round-up of "Two Tribes" problems, the pinnacle of which went something like this:

You are an anthropologist visiting a remote island inhabited by two tribes. Members of one tribe always tell the truth, members of the other always lie. Apart from this detail they are indistinguishable from each other and happily coexist in a prosperous village some distance inland.

To reduce disturbance from visiting anthropologists the natives have built a fork in the one road leading inland from the shore. One path of the fork leads to the village where travelers can be assured of safety and hospitality; the other leads to a dangerous swamp where they will be instantly devoured by voracious giant land-snails.

However, the natives are not unsporting and there is always one of their number stationed at the fork to provide assistance. By ancient tradition you are permitted to ask him or her ONE question which will be answered yes or no. Unfortunately you have lost your Remote Islandese dictionary in the rough sea crossing and, though you have a working knowledge of the language, you cannot remember the words for "yes" and "no". That is to say, you know the words are "pish" and "tush" but you can't remember which is which.

Your problem is to construct one question that you can ask the native at the fork in the road, the answer to which will guarantee that you know which path leads to the comfort and safety of the village and avoids the ravages of the snails.

(PS: I may have made up the bit about the snails...)

Posted at 05:42PM Apr 24, 2007 by John Alderson in Problem Solving  |