Three-way Balance

(Published on 20. November 2025, 09:52 by Kutsumi Hane)

Rules:

Normal Sudoku rules apply, requiring that each row, column, and 3×3 box contains the digits 1–9 exactly once. Additionally:

·Chaos Construction:

Partition the grid into orthogonally connected regions, each containing the digits 1–9 exactly once.

·Tripoints:

No grid point shall be a quadripoint of regions, and all tripoints are given by right-triangle markers:

The two cells touched by the hypotenuse belong to the same region.

The two cells touched by the legs belong to two other regions and must contain digits differing by at least 5, as in a German Whispers constraint.

Example for right-triangle marker:

·Segments:

Every region is cut by the box boundaries into exactly 3 orthogonally connected segments.
Similarly, every box is cut by the region boundaries into exactly 3 orthogonally connected segments.
Each such segment must have a digit sum that is a multiple of 9.

Here you can solve the puzzle online: Solve on SudokuPad
The difficulty is probably somewhere between 4 and 5 stars. I wish you joyful solving!

Hint:

·Filling in digits while deducing region boundaries can facilitate progress.

·The common property(ies) of killer cages of size 3 with sums 9 & 18 may provide useful insight.

Solution code: Digits on the line in row 1.

Solved by marcmees, amaoto, War, mezeji, einalem, zakkai, Marshal on Mars, Piatato, jkuo7, Jasura, gUBBLOR, zonka, Kavman15

Full list

Comments

Last changed on 30. November 2025, 08:42

on 29. November 2025, 11:05 by Piatato
Cool ruleset and a fun puzzle! Maybe it's possible to hide the hints a little better, though (or just omit them entirely?). It's especially a bit annoying that they're part of the rule description inside the puzzle link, as it makes the chances a bit higher that one will accidentally read spoilers. Really enjoyed the puzzle, though!
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Response from Kutsumi Hane: Really happy you enjoyed the puzzle!
I haven't made many puzzles on LMD yet, so I'm still not great with the editing tools, which is why the hints weren't hidden as well as I wanted. Sorry about that. I kept the hints because I hoped they could help more solvers make it to the end — I think finishing a puzzle, even with a small hint, usually makes the experience more fun. Thanks again for commenting!

on 21. November 2025, 01:37 by mezeji
great puzzle. hint helped a lot

on 20. November 2025, 21:33 by War
Very nice puzzle. I think the region building was fun and clever, as my own hint I would recommend doing 80% of the regions before digits

Difficulty:
Rating:	95 %
Solved:	13 times
Observed:	0 times
ID:	000Q7R

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