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?

We have had a go at this puzzle for almost two full weeks (it will soon roll off the display list), and do not seem to arrive at any consensus on an interpretation, let alone a solution.  Perhaps, as the proposer, you could weigh in on this one.  I assume you had something more in mind than reducing the obvious 16 days by a single day (or two?).  A large part of our difficulty, I think, comes from trying to grasp in a realistic way the scenario you present.

 

Posted by ed bottemiller on 2008-09-05 17:00:58