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Sudoku Grid

Those are all of the numbers you need. No, I did not forget any.

  • Normal sudoku rules apply.
  • All numbers, except for 1's and 9's, are queens with respect to themselves.
    • E.g. 2's have the queen's constraint against other 2's but not against 3's.
  • All numbers must be rotationally symmetric with respect to their counter part on the other side of 5.
    • Aka, 1 with 9, 2 with 8, 3 with 7, 4 with 6, and 5 with itself. See below image for an example.
  • Not all 2's are next to non-queens in the top three sudoku squares. Aka, the white sudoku squares in the image below.
  • All 2's must be next to a 4 in the three middle sudoku squares. Aka, the three blue sudoku squares in the image below.
  • All 2's must be next to a 3 in the three bottom sudoku squares. Aka, the three red sudoku squares in the image below.
  • If a 2 is surrounded by 3 non-queens, it will see two 9's.
  • Top right corner is not a queen.
  • The queens of 5 dance clockwise.

enter image description here

"Next to" includes above, below, to the side, or diagonally.

This is my first sudoku puzzle, so any feedback would be awesome. Good luck!

EDIT Apologies, I noticed another symmetry within the puzzle that needed defining to gift a unique solution. I've added 1 last rule at the bottom to account for this.

HINTS

r1c3, r2c9, r3c4, r4c8, r5c5

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  • $\begingroup$ Is "next to" also diagonally? $\endgroup$ – Jens Sep 20 '20 at 19:19
  • $\begingroup$ Yes, I'll amend the description to be a bit clearer. Thanks. $\endgroup$ – user3303504 Sep 20 '20 at 19:22
  • $\begingroup$ And "rotationally symmetric" means "at a multiple of 45 degrees within each 3x3 box", correct? $\endgroup$ – Jens Sep 20 '20 at 19:28
  • $\begingroup$ No, it means the entire sudoku grid could be rotated and the numbers would fall onto their counterparts perfectly. According to Wikipedia its "Automorphic", but I wasn't sure about using jargon ( en.wikipedia.org/wiki/Mathematics_of_Sudoku#Automorphic_Sudokus ) $\endgroup$ – user3303504 Sep 20 '20 at 19:32
  • $\begingroup$ So rotationally symmetric means a 2-fold symmetry (180 degrees), not a 4-fold (90 degrees) symmetry. What do you mean by "dance clockwise"? $\endgroup$ – Jaap Scherphuis Sep 21 '20 at 13:59
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I wrote a program to solve this. I found 15 solutions. Here are two of them. As the solution should be unique, I tried to hunt for violation of the rules. But I could not found any.

  8  9  5 |  6  7  2 |  3  4  1
  1  7  2 |  3  4  8 |  6  9  5
  3  4  6 |  5  9  1 |  2  7  8
----------+----------+---------
  7  2  3 |  1  8  6 |  9  5  4
  4  8  9 |  7  5  3 |  1  2  6
  6  5  1 |  4  2  9 |  7  8  3
----------+----------+---------
  2  3  8 |  9  1  5 |  4  6  7
  5  1  4 |  2  6  7 |  8  3  9
  9  6  7 |  8  3  4 |  5  1  2


  6  1  5 |  3  2  4 |  8  7  9
  9  2  4 |  8  7  6 |  3  1  5
  8  7  3 |  5  1  9 |  4  2  6
----------+----------+---------
  2  4  8 |  9  6  3 |  1  5  7
  7  6  1 |  2  5  8 |  9  4  3
  3  5  9 |  7  4  1 |  2  6  8
----------+----------+---------
  4  8  6 |  1  9  5 |  7  3  2
  5  9  7 |  4  3  2 |  6  8  1
  1  3  2 |  6  8  7 |  5  9  4
 

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  • $\begingroup$ "All numbers must be rotationally symmetric with respect to their counter part on the other side of 5." on the first line of your first solution you have "8 9 5 6 7" but 8 is not the counterpart of 7 and 9 is not the counterpart of 6. $\endgroup$ – Stef Sep 30 '20 at 11:06
  • $\begingroup$ @Stef this is not how I read that condition. I though it meant that the top-left 8 has their counterpart in the bottom-right 2 etc $\endgroup$ – daw Sep 30 '20 at 11:15
  • $\begingroup$ @daw okay, you put my programming skills to shame! I thought I had checked all possibilities as well but clearly not. FYI, the first sudoku you put up was the intended solution. $\endgroup$ – user3303504 Oct 2 '20 at 8:38

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