  In 1946, Koopman introduced a two-sided search model. In this model, a
searched object is active and can move, at most, one step after each test. We
analyze the model of a combinatorial two-sided search by allowing more moves of
the searched object after each test. We give strategies and show that they are
optimal. We consider adaptive and non-adaptive strategies. We show the
surprising result that with the combinatorial two-sided search on a path graph,
the optimal non-adaptive search needs the same number of tests as the
corresponding adaptive strategy does. The strategy obtained can also be used as
a encoding strategy to sent the position of a moving element through a
transmission channel.
