Fantasia on a Theorem of Phistomefel
(Published on 13. July 2025, 23:28 by Md88keys)
by Md88keys
Play in Sudokupad
Phistomefel's theorem might not prove to be true for every irregular 8x8 sudoku, but this puzzle was composed to display the same patterns in an unexpected grid.
Place the digits 1-9 in the grid without repeating a digit in any row, column, or marked region (7 or 9 cells). Each digit in an orange cage must appear once in the center green cage.
Each digit in the blue corner cages must appear in the ring of purple cages, exactly the same number of times it appears in the corner cages.
Digits may not repeat in a cage, and sum to the number given.
Cells a knight's move apart may not contain the same digit.
Solution code: Row 5
Comments
on 21. July 2025, 19:27 by Md88keys
Hey everyone, after some feedback from solvers, I suggest you disable conflict checker for this puzzle.
on 21. July 2025, 18:20 by Dolgubon
The sudokupad solver conflict checker really does not like this puzzle. For example, putting a 2 at r1c1, and a 2 at r2c8 causes sudokupad to say there's a conflict when there isn't any.
--I realize now that I didn't test with the conflict checker. With some of these puzzles with unique rules, I used sudoku maker and the graphics in ways that trick the system. The conflict checker believes that all blue cells are a region, which is not true but was necessary for the graphics.
Fyi the solver would say the puzzle is broken because some of the elements I used to create it are impossible. But if you follow the rules given, you will arrive at the correct solve.
on 14. July 2025, 23:57 by Exigus
That was quite hard. Probably missed some logic but a lot of notes on the side helped a lot (and I don't mind it). Had a good time. Thanks!
on 14. July 2025, 21:15 by Mozart40
@SudokuFan: OMG. Somehow I was thinking of a 23 cage with 3 numbers and therefore thought that the 4 wouldn't work at all. I'm getting old.
on 14. July 2025, 15:37 by PierreTombal
Oops! I made it extra difficult for myself by missing the part in the rules where it said that orange and green are the same digits.
on 14. July 2025, 10:26 by Snookerfan
Very nice! If there was a meta-thing to be discovered, then I missed it. Still a very enjoyable solve. Thank you
on 14. July 2025, 07:59 by SudokuFan
Mozart40, 4+6+5+8 is 23, as you can check with a calculator
on 14. July 2025, 07:43 by Mozart40
One question to the orange cages. They're look like one-cell cages. But they do not sum up to the green cage. Do I miss something?
