Another Form of Matrix Nim

Abstract

A new form of 2-dimensional nim is investigated. Positions are rectangular matrices of non-negative integers. Moves consist of chosing a positive integer and a row or column and subtracting the integer from every element of the chosen row or column. Last to move wins. The $2\times1$ case is just Wythoff's Game. The outcomes of all $2\times2$ positions are found in both the impartial and partizan cases. Some hope is given of being able to solve sums of $2\times2$ games in the partizan case.