Dynamic One-Pile Blocking Nim

Abstract

The purpose of this paper is to solve a class of combinatorial games consisting of one-pile counter pickup games for which the number of counters that can be removed on each successive turn changes during the play of the game. Both the minimum and the maximum number of counters that can be removed is dependent upon the move number. Also, on each move, the opposing player can block some of the moving player's options. This number of blocks also depends upon the move number.