The Balance of Fire and Water
(Published on 17. March 2026, 15:33 by Mad-Tyas)
Sudoku on:
SudokuPad
Rules:
Sudoku: Fill every row, column and marked 3x3 box with the digits 1-9.
Fire and Water cells: There are nine Fire cells in the grid, exactly one in each row, column and marked 3x3 box and filled with a complete set of the digits 1-9. There also are nine Water cells following the same rules as the Fire Cells. It's possible for a cell to belong to both sets simultaneously. The value of Fire and Water cells is the digit in the cell multiplied with the minimum number of orthogonal steps between the Fire cell and the Water cell within the respective marked 3x3 box. If a cell is Fire and Water cell at the same time it's value is 0 cause the minimum number of orthogonal steps is 0.
Note: As the same rules apply to the set of Fire cells and the set of Water cells, it's not possible or required to decide which of the sets is Fire and which is water.
Region Sum Lines: Values along a blue line sum to the same total within each box a line passes through.This total may be different for different lines.
Kropki Pairs: A black dot connects cells with values in 1:2 ratio. A white dot connects cells with consecutive values. Not all possible dots are necessarily given.
Have fun solving!
Solution code: The values of all Fire and Water cells along the positive diagonal (r9c1 --> r1c9).
Comments
on 26. March 2026, 02:17 by Altynbek
Wow, beautiful puzzle. Thanks
on 20. March 2026, 17:03 by War
Excellent puzzle as always Mr Tyas. Easy to make a mistake in the first bit, but easy to correct. Beautiful how the kropki disambiguated and unraveled the puzzle so quickly.
on 19. March 2026, 06:46 by awwkaw
This was a very fun puzzle. Took me a long while to crack it open, but it was very fun to see how the water and fire push each other about 8-)
on 18. March 2026, 22:51 by PuzzlePatzer
That was a lot of fun! (Actually 90 minutes of it :) ) Thanks for sharing.
on 18. March 2026, 15:45 by lmdemasi
Very cool puzzle with great interactions.
on 17. March 2026, 20:15 by mihel111
Great design with gorgeous symetry. Very good puzzle
on 17. March 2026, 18:08 by bansalsaab
Best solution code for beautiful puzzle.
