Properties, isomorphisms and enumeration of 2-Quasi-Magic Sudoku grids |
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Authors: | Siân K Jones Stephanie Perkins Paul A Roach |
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Institution: | aDivision of Mathematics and Statistics, University of Glamorgan, Pontypridd, Mid Glamorgan CF37 1DL, UK |
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Abstract: | A Sudoku grid is a 9×9 Latin square further constrained to have nine non-overlapping 3×3 mini-grids each of which contains the values 1–9. In Δ-Quasi-Magic Sudoku a further constraint is imposed such that every row, column and diagonal in each mini-grid sums to an integer in the interval 15−Δ,15+Δ]. The problem of proving certain (computationally known) results for Δ=2 concerning mini-grids and bands (rows of mini-grids) was posed at the British Combinatorial Conference in 2007. These proofs are presented and extensions of these provide a full combinatorial enumeration for the total number of completed 2-Quasi-Magic Sudoku grids. It is also shown that there are 40 isomorphism classes of completed 2-Quasi-Magic Sudoku grids. |
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Keywords: | Latin squares Sudoku Enumeration |
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