FBI Agent Alice is hot on the trail of computer hacker Bob, who is hiding in one of 17 caves. The caves form a linear array, and every night Bob moves from the cave he is in to one of the caves on either side of it. Alice can search two caves each day, with no restrictions on her choice.
For example, if Alice searches (1 2), (2 3), ..., (16 17), then she is certain to catch Bob, though it might take her 16 days.
What is the shortest time in which Alice can be guaranteed of catching Bob?
There is some ambiguity in the word "catch". If the search only deduces which cave he is in, has he been caught? For example, if there are only three caves and he is not in the two searched, has he then been caught in the third?