The Period of the subtraction games

Abstract

Subtraction games is a class of impartial combinatorial games, They with finite subtraction sets are known to have periodic nim-sequences. So people try to find the regular of the games. But for specific of Sprague-Grundy Theory, it is too difficult to find, they obtained some conclusions just by simple observing. This paper used PTFN algorithm to analyze the period of the Subtraction games. It is more suitable than Sprague-Grundy Theory, and this paper obtained four conclusions by PTFN algorithm . This algorithm provide a new direction to study the subtraction games' period.