Rotational Symmetry Never 10
(Published on 25. September 2025, 15:27 by RailMan)
This is the 4th puzzle I designed related to rotational symmetry. Please read the rules carefully because it is different to the previous puzzles in this series. Have fun!
Normal sudoku rules apply. Place the digits 1 - 9 once in every row, column and box.
German Whispers: Adjacent values along a green line must have a difference of at least 5.
Killer Cages: Digits is a cage cannot repeat and must sum to the total shown in the top left corner.
Rotational Sums CANNOT be 10: All digits in the grid have a 180 degree rotational opposite. Every digit and its rotational opposite NEVER add to 10.
Eg. If R1C2 is a 4 then R9C8 cannot be 6.
Eg. If R5C4 is a 7 then R5C6 cannot be 3.
Solve Online : Solution Check is enabled
Try the other puzzles in this series
Solution code: Row 9
Comments
on 28. September 2025, 09:53 by Zibl
Fun puzzle, thank you!
on 25. September 2025, 22:07 by Exigus
Nice, a different kind of scanning. Thanks!
RailMan: Thanks, I'm glad you enjoyed it.
on 25. September 2025, 18:37 by jinkela114514
All digits in the grid have a 180 degree rotational opposite.
Does this mean that: For every digit X, there exists ONE AND ONLY ONE digit Y, such that: when you rotate the grid around R5C5, every X will fall onto the cells that contains a Y in the original grid, where X and Y can be the same digit?
RailMan: Thank you for the question. Every cell X has a rotational opposite cell Y when the grid is rotated by 180 degrees (a half circle) around R5C5. Any X/Y pair like this cannot add to 10. The digits in cells X and Y may be the same or different but X + Y is never 10. Eg. If R1C3 was 4 then R9C7 could be 1,2,3,4,5,7,8 or 9 but not 6.
The rotational opposite of R5C5 is itself, so R5C5 cannot be a 5.
I hope that clarifies the rule and happy solving.
