Geodesic
Another form of matrix Nim
The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2
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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.
DOI : 10.37236/1608
Classification : 91A18
Mots-clés : two-dimensional Nim, Wythoff's game, partizan case 
@article{10_37236_1608,
     author = {Thomas S. Ferguson},
     title = {Another form of matrix {Nim}},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {2},
     doi = {10.37236/1608},
     zbl = {0988.91009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1608/}
}
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Thomas S. Ferguson. Another form of matrix Nim. The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2. doi: 10.37236/1608

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