GROUP THEORY AND A NEW SUDOKU GAME

From reading the articles [1] and [2] we became to be interested in understanding the group of transformations on the set of all 9 x 9 sudoku grids. We wanted to understand characteristics of those sudoku grids that had the property where said sudoku grid rotated clockwise by 90o is equal to the sudoku grid acted on by a permutation. This led us to understanding which possible 4,4 cycle permutations were allowed. Through our research we developed theories for how these transformations worked and found how they influenced the rules of the games. We also tried to find what information can be given in order to solve the puzzle. An example puzzle is shown to illustrate the theories and potential of a single puzzle.