Ominoku 5x5
(Published on 13. November 2025, 15:42 by eap314)
Fillomino construction: Fill the grid with regions such that ALL cells contain HIDDEN digits that give the size of their region and ALL constraints are valid under these fillomino digits (a 2-cell 6 cage could be contained within a 3-cell region, a given 2 has to be in a 2-cell region, etc). Regions of the same size do not touch orthogonally.
Partial sudoku: Fill the grid with sudoku digits 1-5 such that digits do not repeat in rows, columns, or fillomino regions and ALL constraints are valid under these sudoku digits.
Digits in killer cages sum to the total indicated and CAN repeat if allowed by other rules.
Digits on an arrow sum to the digit in the attached circle.
Thanks to flutchman and other solvers for playtesting the example:
Note: Fillomino digits and sudoku digits are different. Because of the small region size, it's recommended to use the surface tool to refer to fillomino digits and use numbers for sudoku.
Solution: (combined on left, fillomino only on right)
Now for the 5x5!
Click on the image to play:
Setter's note: this isn't an extremely viable ruleset: it's difficult to understand, it's hard to set, and it's easy to solve. Somewhat useful for snack sudokus like this!
Solution code: Row 4 sudoku digits followed by row 4 fillomino digits (left to right, 10 digits)
Comments
on 16. November 2025, 03:18 by waffles_the_dog
Thanks for clarifying the fillomino rules!
This was a really fun and approachable puzzle. I find penpa's UI irksome to deal with so I made this [fairly nice] version for sudokupad (it includes the solution, though obviously lacking the explicit region checks):
https://sudokupad.app/vrurp1fgz2
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eap314:
I like the explicit fillomino/sudoku, and I agree that penpa is a bit annoying, but I'm used to dealing with it.
As this is modeled after chaos construction, it does seem a little weird to include both puzzles, but it can be better aimed at beginners if I do. I'll make that an option in future. Thank you.
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I found it easier to reason about the relationships if I could build both concurrently, I'm unsure if impacts the difficulty of solving though?
on 14. November 2025, 14:06 by eap314
Updated fillomino rules a few times and made the example easier to understand (and unique). Thanks to GraphZahl81 and SennyK
on 14. November 2025, 13:08 by SennyK
Maybe it could be worth adding example titled "sudoku digits - solution" showing sudoku solution and next to it example titled "hidden fillomino digits - solution" showing fillomino solution with fillomino digits, I think this could really help to understand it faster.
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eap314:
You gave me the motivation to actually update the example. Thank you. I hope this is easier to understand.
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SK: You are welcome, now it is clear! I myself was at first wondering how do I know which digits show the size of region, not understanding that those digits are hidden and have nothing to do with sudoku digits. This is because I never saw a fillomino before.
on 14. November 2025, 09:48 by NXTMaster
Took me a bit to remember the rules for fillomino. For some reason I thought the "regions" in fillomino behaved like [polyominos] with cells not containing anything, but once I remembered the entire region is made up of its size as a digit in each cell, the rules suddenly made sense.
What makes you think it isn't too viable? I think it has potential
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eap314: [thanks, fillomino rules updated]
I thought it'd be hard to wrap your mind around, and for bigger puzzles it's difficult to keep track of how fillomino digits satisfy the constraints. I guess some people really enjoy these snacks though.
In future I might set a factored fillomino puzzle (regions where one is a multiple of the other do not touch orthogonally or maybe orthogonal regions must be coprime)
on 14. November 2025, 04:10 by SennyK
Interesting, must have been hard to set, well done! Thanks
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eap314: This one didn't take too long, but I was a little lucky that I figured out a way to make it unique.
on 13. November 2025, 20:46 by GraphZahl81
For anyone who isn't that familiar with fillomino, it would be nice if you state all fillomino rules. The important rule that two regions of the same size aren't allowed to touch orthogonally is currently not mentioned at all.
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eap314:
I forgot that in the mess of changing the puzzles. Thank you
on 13. November 2025, 20:02 by dzamie
That arrow in the upper-right is quite clever! This one took me a bit, really neat ruleset. I like that you can't *just* solve it as a fillomino, and then as a sudoku; you have to look forward a little to make sure the sudoku will be solvable as you do the fillomino numbers.
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eap314: You can almost solve it entirely with sudoku, but the added fillomino stuff is just more fun. Thanks for the comment!
