Entropic islands
(Published on 1. April 2026, 04:11 by Killer Joe)
Hello.
Normal Sudoku rules apply.
Digits are grouped into entropic sets:
Low → {1, 2, 3}
Mid → {4, 5, 6}
High → {7, 8, 9}
A digit placed in a circle indicates the size of the orthogonally connected group of cells that all contain digits from the same entropic set as that digit.
No group contains more than one circled cell.
Not all groups contain a circle.
Digits separated by a white dot must be consecutive.
Digits separated by a black dot have a 2:1 ratio.
Have fun.
Solution code: Row 9, first 6 digits.
Comments
today, 06:22 by Gankra
Oh wow this ruleset and how you used it was an absolute dream. Deeply satisfying to realize how constrained things are. Often this kind of "regions must grow from circles" puzzle has more fighting tooth and nail over why something must go left or right but this kept it so simple and clean!
today, 01:12 by Killer Joe
Changed 'regions' to 'groups'.
yesterday, 23:46 by VolpeRosso
Wonderful puzzle! I agree with KJ though - I think it needs a constraint such as "no two regions of the same entropy may touch orthogonally". Otherwise, a cell of the same entropy *may* be "touching" a region, but be in a different region. <3
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Oh, I used 'groups' first as a description and later 'regions'.
That is definitely a mistake on my part that I hadn't noticed before. I can see how that could cause confusion. Grts, Jonesy.
yesterday, 18:39 by prismoid
Beautiful fun logic. Puzzle also solves uniquely without the "every region contains up to one circle" constraint for a 2.5-3 star challenge
yesterday, 18:24 by KJ_for_science
Nice puzzle. The rules should however be adapted stating precisely that no cells orthogonally connected to a region can contain the same entropic digit as the region itself. Otherwise the puzzle is not solvable.
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The digit in the circle indicates the size of the region. Connecting another cell would change the size of the region. So yes, there is a negative constraint but I don't think that should be explicitly stated in the rules. Grts, Jonesy.
yesterday, 15:20 by Gankra
Oh wow this ruleset and how you used it was an absolute dream. Deeply satisfying to realize how constrained things are. Often this kind of "regions must grow from circles" puzzle has more fighting tooth and nail over why something must go left or right but this kept it so simple and clean!
yesterday, 15:19 by Franjo
Thank you very much for creating and sharing this beautiful puzzle with an interesting ruleset.
yesterday, 09:42 by Fizz
That was fun, thanks a lot!
on 1. April 2026, 19:18 by ofsmul
Took me a while to get started, but then the flow was lovely. Great puzzle, thanks!
on 1. April 2026, 14:20 by Dcs
very approachable with beautiful logic
on 1. April 2026, 05:33 by Dermerlin
I loved the ruleset.
I loved the (only 6 digit) solution code.
I loved the puzzle.
