International Journal of Combinatorics
Volume 2012 (2012), Article ID 760310, 6 pages
Research Article

The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group

Department of Computing and Mathematical Sciences, University of Glamorgan, Pontypridd CF37 1DL, UK

Received 10 May 2012; Accepted 28 September 2012

Academic Editor: Martin Kochol

Copyright © 2012 Siân K. Jones et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A Sudoku grid is a constrained Latin square. In this paper a reduced Sudoku grid is described, the properties of which differ, through necessity, from that of a reduced Latin square. The Sudoku symmetry group is presented and applied to determine a mathematical relationship between the number of reduced Sudoku grids and the total number of Sudoku grids for any size. This relationship simplifies the enumeration of Sudoku grids and an example of the use of this method is given.