Blue lines are region sum lines. For each line, digits on the line have an equal sum N within each box it passes through. There are 4 lines that cross another line in this puzzle. These are to be treated as independent lines. (So there are 8 lines in total here)
Cells separated by a black Kropki dot are in a 1:2 ratio. Sets of digits separated by a black Kroopki Doot (a long, ellipse-looking shape) must have their respective sums be in a 1:2 ratio.
Cells separated by a white Kropki dot are consecutive. Sets of digits separated by a white Kroopki Doot must have their respective sums be consecutive.
Not all Kropki or Kroopki Do(o)ts are necessarily given. There is no negative constraint.
Solution code: Row 3 and Column 3:
on 15. February 2026, 09:17 by NumberCruncher
Great Dot-Doot-Logic here! For me the direction of the doots was clear once I looked at it as two dots that have later been connected. Took me 10:03 then.
on 31. January 2026, 20:27 by tiwe
since the long kropkis are 2x2 there is no "natural" direction saying with cells go into the sums together, so you should clarify in the rules, but i can't find easy wording for it. you could draw cages (without given sums) around R1C12, R2C12, R23C5, R23C6 each and say the kropki rule applies to the cage sums.
having each direction of region sum line in a different colour might also help understanding the rules.
on 19. June 2025, 21:32 by Vaaletee
very good i liked it
on 23. December 2024, 21:13 by mau
Very satisfying. Especially liked the two long pills and their place in the logic. Thanks for this colorful puzzle.
Sandra here! Thank you :) happy you enjoyed the puzzle
on 29. September 2024, 13:10 by BabyfacedBard
Lovely puzzle! More of a 1.5-2 star difficulty in my view, but very satisfying as usual
on 5. August 2024, 15:44 by PaganiusI
Took me 5 tries or something, because my brain couldn't handle these pills. Still a really fun puzzle
on 15. June 2024, 18:29 by nlanday
really lovely puzzle, as always! I think the instructions would be clearer if they clarified which direction the doots should be read.
on 16. January 2024, 23:39 by eggfriedcheese
Lovely Puzzle! Loved getting the crayons out!
on 11. September 2023, 06:35 by MrRobotMan
This puzzle was graat! My only struggle was due to doing some really bad math near the end.
on 26. July 2023, 23:19 by Ratfinkz
Got there!!! Loved this, despite making a wrong logical leap several times on the trot!!
on 14. July 2023, 02:04 by Wessel Strijkstra
hella cute<3
on 10. July 2023, 22:40 by Jreg
Heyyy so I just published a puzzle directly inspired by this one. I call it The Butterfly Defect and I worked in the pattern that I first THOUGHT I saw in your grid. Feel free to give it a try as well! (:
on 10. July 2023, 09:18 by SandraNala
After some valuable feedback from solvers I have added to the rules that the 4 crossing lines have to be seen as independent and therefore 8 lines exist in this puzzle. Thank you for pointing that out! :)
on 10. July 2023, 00:24 by Nordy
Very cool!
on 9. July 2023, 23:32 by HumanBirdsong
Neat!
on 9. July 2023, 23:30 by Jreg
...and then I solved it in under five minutes, lol. Just to redeem my intelligence.
on 9. July 2023, 23:22 by Jreg
Can you please clarify in the description that the crossing renbans are NOT all parts of one big renban? I literally spent an hour thinking they were all connected before I figured out the puzzle couldn't be solved that way.
Sandra here! Thank you for pointing that out. I changed the rules of the puzzle to make that clear now! Glad you still managed to solve it in the end. Hope you enjoyed it!
on 9. July 2023, 15:51 by dumediat
Clever and fun, thanks!
| Difficulty: | ![]() |
| Rating: | 92 % |
| Solved: | 411 times |
| Observed: | 20 times |
| ID: | 000EFD |
Please note: The German version of this page has changed. It is possible that this page does not contain the latest information.