2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145335The main problem addressed here is to decide whether it is possible or not to go from a given position on a peg-solitaire board to another one. No non-trivial sufficient conditions are known, but tests have been devised to show impossibility. We expose the way these tests work in a unified formalism and provide a new test which is strictly stronger than all previous ones.27 pages, 31 figuresCombinatoricsAlgebraic Geometry05A99 (Primary) 91A46, 52B12 (Secondary)text