  Motivated by recent single molecule studies of proteins sliding on a DNA
molecule, we explore the targeting dynamics of N particles ("proteins") sliding
diffusively along a line ("DNA") in search of their target site (specific
target sequence). At lower particle densities, one observes an expected
reduction of the mean first passage time proportional to 1/N**2, with
corrections at higher concentrations. We explicitly take adsorption and
desorption effects, to and from the DNA, into account. For this general case,
we also consider finite size effects, when the continuum approximation based on
the number density of particles, breaks down. Moreover, we address the first
passage time problem of a tagged particle diffusing among other particles.
