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?

The point of the problem is not to find a reasonable argument for why you and the enemy are doing what you are doing. It's not hard to do in problems like this if you assume the people are normal, but who ever said that? Crazy reasons like "you have a fear of searching more than two caves per day" and "the enemy has a fear of staying in the same cave" could be the case.

There's people who tell the truth all the time, and other even stranger disorders in order to make the solving the logic part of the problem more interesting.

Posted by Gamer on 2008-08-25 23:17:02