  Koopman introduced two-sided search models. In this search model, the
searched object is active and can move one step after each test at most. In
this paper we analyze the model of a combinatorial two-sided search by allowing
more moves of the searched object after each test. We give search strategies
and show that these strategies are optimal. We consider adaptive and
non-adaptive strategies. We show the surprising result that with the two-sided
search on a path graph the optimal non-adaptive search needs the same number of
questions like the corresponding adaptive search strategy does.
