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Did you check for rotational and mirror symmetry? As in, are the 12 unique sudokus just the same one, rotated in 4 ways, and mirrored along the x or y axis?
by redfast00 19d ago
Did you check for rotational and mirror symmetry? As in, are the 12 unique sudokus just the same one, rotated in 4 ways, and mirrored along the x or y axis?
- probably_wrong 19d agoI was wondering this myself so I wrote a script that shows that there are duplicated puzzles if you count a rotated Sudoku as being equivalent. Here's one example: Puzzle 2 is 1234 3412 2341 4123 If you rotate it counterclockwise you have 4213 3142 2431 1324 And if you normalize it, replacing the first row with "1234" (brilliant idea from the post), you get 1234 4312 2143 3421 Which is listed as puzzle 7. A quick check gives me that puzzles 1, 2, 3, 5, 11 and 12 would be unique under rotation, but I wrote that check in five minutes so there must be bugs somewhere. Also, I performed no check for mirror symmetry whatsoever (update: I did a quick one, same result). I don't want to miss my chance to say that the post is brilliant and that it convinced me to leave what I was doing to check for rotations. I was nerd sniped in the best way and I take my hat off for the OP.