Philosopher's football

Combinatorial games are games where the players alternately take moves. In the game we do not have any chance devices that could impact on the game randomly. Players have complete information about past moves to decide how to play on. The rules are such that the game must eventually end. Philosopher’s football or Phutball is a not so well-known combinatorial game which is the focus of this work. We present why the game is difficult and why determing whether a player can win in a given situation in one move is an NP-complete problem. We prove it by reducing to an already known NP-complete problem 3-SAT. We have also implemented Phutball application for two players, which is accessible through a web browser