  In this work we consider the problem of searches that utilises past
information gathered during searching, to evaluate the probability distribution
of finding the source at each step. We start with a sample strategy where the
movement at each step is in the immediate neighbourhood direction, with a
probability proportional to the normalised difference in probability of finding
the source with the present position source finding probability. We evaluate a
lower bound for the average search time for this strategy . We next consider
the problem of the lowerbound on any strategy that utilities information of the
probability distribution evaluated by the searcher at any instant. We derive an
expression for the same. Finally we present an analytic expression for this
lower bound in the case of homogeneous diffusion of particles by a source. For
a general probability distribution with entropy-E, we find that the lower bound
goes as exp(E/2).
