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)
I also found the mise-en-scene unrealistic, and in a sense it has too much information given or too little. Can each side (we and the enemy) know what the other is doing? It seems that it is assumed because the enemy moves at night, that they are undetectable. Why would we move only in daylight -- since presumably the caves are dark in any time of day? Why would we not watch all the entrances 24/7? Is there just one individual enemy, else why would all be in the same cave, and move therefrom en masse? Perhaps they have an invisibility potion?
I am willing to consider the puzzle as posed, but if all those who have "solved" it have to offer is a reduction of one day (or PERHAPS two -- see my last rejoinder) from the 16-day worst-case scenario, I think the problem lacks inspiration. I hope to see someone (without "cheating" on the specs) who can really substantially reduce the upper limit of required search days. Perhaps it is time for the poser of the problem to state whether there is more to be done with this one. On the other hand, the Pentagon has been engaged in some such chase for years, though with many other variables to consider....
re(3): interesting question
