  Prudent walks are self-avoiding walks which cannot step towards an already
occupied vertex. We introduce a new model of adsorbing prudent walks on the
square lattice, which start on an impenetrable surface and accrue a fugacity
$a$ with each step along the surface. These are different to other exactly
solved models of polymer adsorption, like Dyck paths, Motzkin paths and
partially-directed walks, in that they are not trivially directed - they are
able to step in all lattice directions. We calculate the generating functions,
free energies and surface densities for this model and observe a first-order
adsorption transition at the critical value of the surface interaction.
