![]() ![]() ![]() We can reduce the number of morphs required by a factor of 8, I think, so we don't waste time checking transposes/rotations, but that is still 419,904 morphs per grid. We can simply count the number of ED Sudoku grids that can be morphed into a SudokuX grid.Įach of the 5.47 billion ED S-grids needs to be morphed in all ways possible. Ok, how to answer Leren's question 2, ie how many ED SudokuX grids? We agreed, I think, that ED ( essentially different) grids will always refer to comparisons made using the standard set of 3,359,232 transformations that morph one Sudoku grid into another.ĮS makes sense as an abbreviation for "not ED", thanks Leren. Thanks largely to dobrichev's fabulous fsss2 solver, I counted them all in 4 threads x 6 hours. Minimum clue counts: it is known that 12-clue puzzles exist, so the first question here is, are there 11-clue SudokuX puzzles?įinally, I determined the number of grids above by the '1's-template method (there are 1040 templates). The only alternative appears to be checking the 5.47 billion ED Sudoku grids to deterimne which have SudokuX isotopes, but that's still a daunting task. But we have here around 1,000 times the number of grids, so SudokuP methods that took just a few days would take years here (not to mention the 5TB of disk space we'd need to hold all the grids). We were able to count ED SudokuP grids because the grids that needed checking are not too numerous. We can (and probably will) calculate the number of SX-different grids, but the exact number of ED grids will of course be less than that. We can't use McGuire's method (Burnside's Lemma) because of the orbit connection problem. It now becomes clear why nobody seems to know how many ED SudokuX grids there are. We can also permute Band2/Stack 2 to give a 180-degree rotation of the center box. There are 6 ways to tweak a grid so that the diagonals in the corner boxes are permuted but not shifted. There are, it seems, just 12 of these (x 8 for rotation/reflection, giving 96 in all). My guess is around a billion, but I do hope to come up with an accurate figure for the number of SX-different grids at some stage soon.Īs we did for SudokuP, we define SX-equivalence in terms of the subset of Sudoku transformations that preserve the diagonal property. Given that number appears nowhere relevant on the Web, I am either wrong, or nobody has counted them before.Īh, I hear you say, but how many essentially different SudokuX grids are there? How many different SudokuX grids there? I think the answer is (up to relabelling) 153,255,603,504. Mysteriously, while it is a popular variant, it seems, little is known about the numbers. Following a suggestion from Leren, I have also been looking at standard SudokuX, ie Sudoku with distinct values along both diagonals. ![]()
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