Ruled by a king, ruled out by his knights
(Published on 27. September 2025, 02:07 by adalg)
I watched a video on the zetamath sudoku setting stream and couldn't resist checking the sudokumaker.app site. I immediately got hooked. Here’s the outcome. I wanted to make something out of the ordinary so I chose some rules which I don’t know if others have introduced before; if so they may exist with other names. My thanks to zetamath for demonstrating, and to sirxemic for his wonderful and user friendly sudoku maker. I loved the Preferences: Advanced: Cosmetic lines with grid-resolution-10 option, for drawing.
Rules:
Normal sudoku rules apply, plus:
1) Matching pairs. Any digit on a "pairline" appears exactly twice on that line. Blue and red is just for disambiguation.
2) Parity-squarity cages. All numbers in a cage are of the same parity (all even or all odd) and sum up to the square of one of them. They may repeat if allowed by other rules.
3) Peaceful pieces: To be at peace with itself, each chess piece (in this puzzle, a king and four knights) considers all locations it could move to in their next turn on a chess board and scans them for the possibility of two or more elements (cells) summing up to its own value. These elements need to be in touch with one another (each adding ortho- or diagonally to a previous one) and their assembly may, or may not, touch the chess piece itself. (It’s like an invisible >1 cell arrow in an "arrow equals circle" rule, and possibly detached from its circle).
4) Math symbols for inequality have conventional meaning (open toward a higher value and point their tip to the lower one).
For clarification of rule 3: As an example, if a queen were positioned at R1C8, the combination of e.g. R3C6+R2C7+R2C8 could serve as a cluster and the R3C6 could possibly be identical to one of the others.
Solve here: Sudokupad link
I hope you'll like it!
Solution code: Enter digits in row 1, from left to right, without spaces.
Comments
today, 00:43 by adalg
I've revised the phrasing of rules, and the drawing (I didn't know how to enter unicode characters for the pieces but I hope the king is easier to identify now). I inserted an updated link to the online solving (with the revisions).
yesterday, 20:00 by adalg
For those who have solved the puzzle and have access to hidden comments, I've added there a dropbox link to a pdf showing my intended solving path. I considered there whether a king or bishop in R1C3 would make a difference. You don't have to sign in to dropbox, just download the pdf from the site.
yesterday, 16:55 by adalg
@mezeji: Wow, this is exciting! Set with a bishop in the kings position at R1C3, I tried and found a solution that was identical to my original intention. Following a different solving path. What a coincidence! But you mean that somehow a yet another solution is possible if R1C3 was a bishop? I'm keen on discussing this further in the hidden comments, if you like. Now I feel lucky to have introduced the puzzle with the confusing king figure. I guess no one would have studied the bishop possibility otherwise.
yesterday, 11:20 by mezeji
For the "right" sollution figure in R1C3 is considered a King. (bishop gives another solution)
on 27. September 2025, 14:50 by adalg
Tried to improve some explanations.
on 27. September 2025, 14:40 by adalg
I tried to provide text for the German version, I hope it looks ok.
Habe versucht, Text für die deutsche Version bereitzustellen, ich hoffe, das ist ok.
on 27. September 2025, 13:16 by adalg
@Basil: Thank you for your feedback! I didn't know about the unicode-characters and apologize if the figures are confusing. For clarification of rule 3: If there is a possibility of more than two cells forming a cluster, each cell does not have to touch all the others. If a queen were positioned at R1C8, the combination of e.g. R3C6+R2C7+R2C8 could serve as a cluster and the R3C6 could possibly be identical to one of the others.
on 27. September 2025, 10:30 by Basil
Tip: There are unicode-characters for the chess pieces, which you can use. From the puzzle title I presume the piece in R1C3 is a king, though from the picture I would have guessed queen or bishop.
Could you please clarify rule 3; maybe give an example. All digits touch each other orthogonally or diagonally. Do they have to be identical?
