  We consider a discrete time simple symmetric random walk on Z^d, d>=1, where
the path of the walk is perturbed by inserting deterministic jumps. We show
that for any time n and any deterministic jumps that we insert, the expected
number of sites visited by the perturbed random walk up to time n is always
larger than or equal to that for the unperturbed walk. This intriguing problem
arises from the study of a particle among a Poisson system of moving traps with
sub-diffusive trap motion. In particular, our result implies a variant of the
Pascal principle, which asserts that among all deterministic trajectories the
particle can follow, the constant trajectory maximizes the particle's survival
probability up to any time t>0.
