You are hot on the trail of an enemy, who is hiding in one of 17 caves.

The caves form a linear array, and every night your enemy moves from the cave he is in to one of the caves on either side of it.

You can search two caves each day, with no restrictions on your choice. For example, if you search (1, 2), (2, 3), ..., (16, 17), then you are certain to catch him, though it might take you 16 days.

What is the shortest time in which you can be guaranteed of catching your enemy?

(In reply to question by Gamer)

Is your last paragraph suggesting that there is a "liars" angle in this puzzle? Is it irrelevant to try to "make sense" of the situation as suggested?  If this proposer is just teasing, perhaps he could join in, since discussion seems to have died out after the weak proposal to cut the search from 16 days max to 15 (or 14?).

The problem does not explicitly state that the two-a-day searches are the ONLY option we have. Perhaps we are free to invent our own: e.g. we can guarantee capture (or more likely death) of the enemy within ONE day by simply tossing a blockbuster (or weapon of our choice) into all seventeen caves. This was posted as a "logic" problem, but who knows??

Posted by ed bottemiller on 2008-08-28 19:01:05