One of the big sudoku questions was: How many completed Sudoku grids are there? This was answered, see http://www.shef.ac.uk/~pm1afj/sudoku/ The answer is 6670903752021072936960. Call two completed sudoku grids "equivalent" if one can be obtained from the other by a sequence of the following operations: 1) permutation of the digits 1-9 2) permutation of the rows. These come in two types: a) permute the three rows within a given band b) permute the bands 3) permutation of the columns, same two types. 4) rotation, reflection A sequence of these transformations that maps a grid to itself is called an automorphism of the grid. Example: 124|567|893 378|294|516 659|831|742 ---+---+--- 987|123|465 231|456|978 546|789|321 ---+---+--- 863|972|154 495|618|237 712|345|689 the permutation (1397)(2684) on the digits followed by a clockwise rotation through 90 degress is an automorphism. Question: what are the possible automorphism groups? Or equivalently, how many sudoku grids are there up to equivalence? This has been answered, see http://www.shef.ac.uk/~pm1afj/sudoku/sudgroup.html Now: is this helpful in the problem of searching for a sudoku puzzle with 16 clues? I think fated sets are invariant under an automorphism. Therefore we only need choose one grid from each equivalence class and compute all the fated sets. Unfortunately there are 5472730538 equivalence classes. Anyway, in the computer search for a 16, we don't want to choose two grids that are equivalent. Gary McGuire