2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/30373We show that, in John Conway's board game Phutball (or Philosopher's Football), it is NP-complete to determine whether the current player has a move that immediately wins the game. In contrast, the similar problems of determining whether there is an immediately winning move in checkers, or a move that kings a man, are both solvable in polynomial time.9 pages, 8 figures. Revised to include additional references on the complexity of checkersComputational ComplexityComputer Science and Game TheoryF.1.3,K.8.0text