2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110136We prove that there does not exist a subset of the plane S that meets every isometric copy of the vertices of the unit square in exactly one point. We give a complete characterization of all three point subsets F of the reals such that there does not exists a set of reals S which meets every isometric copy of F in exactly one point. A finite set X in the plane is Jackson iff for every subset S of the plane there exists an isometric copy Y of X such that Y does not meets S in exactly one point. These results are related to the open problem: Q. (Steve Jackson) Is every finite set X in the plane of two or more points Jackson?Latex2e: 23 pages Latest version at http://www.math.wisc.edu/~millerLogicMetric Geometry52C20, 05C12, 11H06text