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

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... e 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. Email: n.beaton@usask.ca, giliev@chem.utoronto.ca 1 One can instead associate the fugacity with vertices in the surface, to obtain a slightly different model.