What Goes Around (Killer + Entropic Lines)
(Published on 14. January 2026, 16:25 by sujoyku)
Rules:
- Normal sudoku rules apply, i.e. each row, column, and 3x3 region has to contain the digits from 1 to 9 once each.
- Entropic Lines: Any three adjacent digits along a peach line must contain one low digit (1, 2, or 3), one medium digit (4, 5, or 6) and one high digit (7, 8, or 9).
- Killer Cages: Digits in a cage must sum to the clue in the top left.
- Kropki: Digits joined by a black dot have a 1:2 ratio. (Not all dots are given.)
Here you can solve the puzzle online:
Solution code: Column 5 from top to bottom (9 digits in total)
Comments
on 15. January 2026, 13:53 by Franjo
Eine Komposition von zeitloser Eleganz! Vielen Dank für das herrliche Puzzle.
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Vielen Dank für deinen Kommentar, Franjo! Es freut mich sehr, dass Dir das Rätsel so gut gefallen hat.
Herzliche Grüße, sujoyku
on 15. January 2026, 08:47 by VitP
To determine whether a puzzle falls into the level 2 category, a good question to ask is "could a non-expert solve this, using only standard procedures ?" here, the answer is YES.
0) There is a way to "brute force" solve this, simply by colouring every cell where you find ANY restriction. This results in the entire grid being coloured as LM, LH, or HM, and then you have to reduce everything, which is pretty tedious. there is a better way.
1) A quick inspection of the puzzle shows that there is nothing to "bite on" directly. So you entropy-colour the longest line. And this produces a full entropy set in r8 and c2.
1a) In r8, if the set is LOW, the 9 cages cannot be filled.
1b) In c2, if the set is HIGH, the 11 cages cannot be filled.
1c) DELETE the colouring on the rest of that line. It is not really helpful at this time, and adds clutter.
2) study r8. you can place 4 digits, and lots of restricted candidates.
IMPORTANT: do NOT replace the colour for the medium entropy with the candidate set, because the objective here is to MINIMIZE CLUTTER.
3) study c2. you can get 3 more digits, plus some candidates.
Now, for the rest of the puzzle, when you determine the entropic state of a cell EXACTLY, colour it. specifically, you now have 3L, 6M, 2H.
4a) consider box 3. If the kropki cells are {1248}, add 12, this breaks the box. thus you locate a 36 k-pair.
4b) continue to study box 3, and fill in the candidates.
5) the 8 in box 7 is on the line.
6) study r1. this locates the low cells on the short line.
7) consider the 4 cells of the same entropy on the medium line.
7a) if they are HIGH, the 15 cage breaks.
7b) from r1, we know they aren't LOW.
8) work on c9.
9) study box 6. the 15 cage must include a medium.
After this, you are doing BASIC SUDOKU, NOT COLOURING. When you determine that c5r6 is LOW, you should be home free.
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Thank you for your comment, VitP! I am glad that you like to engage in the discussion of this puzzle. Can you please make comments hidden that involve such an amount of information on the solving strategies? Otherwise people might read it accidentally and feel spoilered.
Kind regards, sujoyku
on 15. January 2026, 07:18 by superkinkel
Excellent puzzle, thank you! Going back and forth between the different constraints was extremely nice and entertaining. I think it’s rather on the three star side.
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Thank you for your comment, superkinkel! I am glad that you enjoyed the solve. Also thanks for sharing your take on difficulty.
Kind regards, sujoyku
on 15. January 2026, 02:36 by antiknight
Cool and easy! 1 star tho ^^
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Haha, if this is 1 star, I don't want to be in the same room with a puzzle that you'd call 5 stars. :D
But without kidding: Thank you for your comment!
Kind regards, sujoyku
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Haha! Its rated as 2 stars tho so its really close :P. You are welcome :)
on 15. January 2026, 01:12 by cygne
Loved this one! Kudos
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Thank you, cygne!
Kind regards, sujoyku
on 15. January 2026, 00:30 by SennyK
Lovely puzzle with nice interactions, thank you! :-)
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You are much welcome, SennyK, thank you for your comment! I am glad that you enjoyed the interactions.
Kind regards, sujoyku
on 14. January 2026, 22:19 by IFlaig
Great puzzle! Nice break in :)
on 14. January 2026, 22:00 by IFlaig
Great puzzle! Nice break in :)
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Thank you, IFlaig!
Kind regards, sujoyku
on 14. January 2026, 21:46 by Myfyr MJ
Very nice but probably nearer 3 stars given the amount of colouring involved.
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Thank you for your comment, Myfyr MJ! I am glad that you enjoyed it. Also thanks for sharing your perspective on the difficulty level.
Kind regards, sujoyku
on 14. January 2026, 20:57 by Exigus
Good fun! A couple of key deductions that were really nice. Thanks!
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Thank you for your comment, Exigus! I am glad that you had a fun solve.
Kind regards, sujoyku
on 14. January 2026, 19:49 by PinkNickels
Some really neat steps along the way!...or else I just missed something really obvious and made it way more complex than need lol :) Thanks for sharing.
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Thank you for your comment, PinkNickels! As I think it is between 2 and 3* (initially uploaded at 3 to be cautious), I don't think you must have missed some easy/easier steps. Anyways, I am glad that you liked the puzzle.
Kind regards, sujoyku
on 14. January 2026, 18:57 by Snookerfan
Fun symmetrical puzzle, I really enjoyed it. Thanks!
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You are much welcome, Snookerfan, thank you for commenting! It is great to know you enjoyed the puzzle.
Kind regards, sujoyku
on 14. January 2026, 17:37 by ScatterBrain
Good interaction between the cages and the entropic lines!
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Thank you for your comment, ScatterBrain! I am glad that you liked those interactions.
Kind regards, sujoyku
