A Bouquet of Complements
(Published on 10. June 2026, 13:36 by RockyRoer)
The Rules:
- [Sudoku]: Normal sudoku rules apply -- fill every row, column, and 3x3 box with the digits from 1 to 9 once each.
- [Dynamic Fog]: Entering enough correct digits in cells will reveal more of the puzzle.
- [Complements]: A pair of 2-digit numbers read from left to right are circled. This pair of numbers must add to 90. Each time the fog clears, another pair will appear - each time summing to 90.
- [Standard Sudoku Variants]: Some (but not all) of the following standard variant sudoku rules may appear:
- [Killer] Digits in a killer cage must sum to the total given in the upper right corner.
- [Lines] Standard line rules will apply for some common line variants that may appear such as:
- Renban - the digits on the line form a set of consecutive numbers
- Entropic - any three digits on the line cycle through the sets {123},{456}, and {789}
- Modular - any three digits on the line cycle through the sets {147}, {258}, {369}
- German whisper - any two adjacent cells on the line have a difference of at least 5
- Dutch whisper - any two adjacent cells on the line have a difference of at least 4
- Parity - any two adjacent cells alternate between odd and even
- [Pairs]: Standard pair rules will apply for some common pair variants that may appear such as:
- XV - cells separated by X sum to 10 and cells separated by V sum to 5
- Kropki - cells separated by a white dot have a difference of 1 and cells separated by a black dot have a ratio of 2:1
The Puzzle:
Try it on Sven's Sudokupad
Solution code: The second to last complements to appear - in numerical order from least to greatest. 4 digits (For example: 2664)
Comments
on 27. July 2026, 15:54 by corrie
Lovely puzzle, and such a clear guided solution path! I tremendously enjoyed it.
I also don’t know where the solution code confusion comes from, with the example you gave it‘s made very clear how the sorting has to happen!
on 24. July 2026, 17:10 by Reina
After solving im reading the comments about confusing code and i was like what, thats the best code ever, short, sweet. Great!
Then i read the description closely and understood. You see, when i entered the code and it worked i havent really read the description, just glanced that its second to last pair and entered it in reading order without thinking and it worked.
Maybe that should be the code description right there ;-)
Other than that, i think it was the best solve i had in months, way too easy but very pleasant to learn while solving. And that twist at the end! Marvelous. Keep up the great work that you do!
on 11. July 2026, 13:53 by wuc
Great puzzle. Fun to solve. Learning while solving is what I love.
on 11. July 2026, 03:22 by barfurth
Really fun puzzle!
I have to agree that the description of the solution code is confusing. It says "from least to greatest", which seems to ask for numerical order, but then the example ("2664") doesn't even match that.
Using the second to last pair to appear can be confusing, for example if one has to interrupt the solve and comes back later to finish.
I did appreciate keeping the code short, so I don't have to keep a long string of digits in my head (or switch back and forth between tabs) to be able enter it. So thanks for that.
Reply: I was thinking of the two digit numbers... so 26 is less than 64.
on 20. June 2026, 21:01 by rhodri
Magnificent, except the solution code
on 16. June 2026, 14:40 by Kattorzeh
Super mega fun!!! (except finding the solution code :V)
on 12. June 2026, 00:17 by SanFranSam
I found the solution code the hardest part of the puzzle. It's the second to last pair of pills top pill first, left to right. Then second pill.
on 11. June 2026, 22:04 by greemi01
i think the solution code is off. i found it to be the second to last complements to appear left to right, top to bottom (not numerical order)
on 11. June 2026, 21:23 by Rammstein
need a part two. great puzzle.
on 11. June 2026, 05:00 by Decapod
I feel like this requires a deeper understanding of modular arithmetic than I possess.
Reply: That one box will need that - but nothing more. The key concept is to think about what is the remainder the digits when divided by three. {1, 4, 7} all have a remainder of 1. {2, 5, 8} all have a remainder of 2, and {3, 6, 9} all have a remainder of 0. If you consider what happens when you add combinations of these in light of their remainders, and what the remainder NEEDS to be, I hope you will discover what you need to step past that box. If you want a more specific hint, feel free to ask in a comment, or if your on discord hit me up there.
on 11. June 2026, 01:37 by Freegerator
Fun puzzle, thank you!
on 10. June 2026, 21:11 by blackjackfitz
Huzzah!
on 10. June 2026, 20:22 by Franjo
Thank you very much for creating and sharing this nice and approachable math puzzle.
on 10. June 2026, 17:42 by wilsig
Fantastic puzzle!!
on 10. June 2026, 17:06 by pmays123
Very fun. Thanks!
on 10. June 2026, 17:03 by Nylimb
The interactions between the constraints were quite fun. Thanks.
