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 re(2): interesting question by Daniel)

There are 17 caves in a certain island. You arrive on the island, but don't know which cave he is in, and in order to not get lost on the island, you decide to only move around during the day. The enemy knows the layout of the land better than you, so he is able to move at night undetected.

However, the caves are fairly well dispersed and far apart on the island, and he doesn't want to be seen during the day, when you could spot him easily. The caves are situated such that he can only move to 2 from 1 before daybreak, or from 2 to 1 or 3 or... 17 from 16. (Note he has to sleep during the day, and thus he doesn't move while you are inspecting the two caves during the day)

Posted by Gamer on 2008-08-25 23:12:29