✧ Magically Modifying Loop ✧
(Published on 25. November 2023, 06:30 by ElChiglia)
---- RULES ----
Normal Sudoku rules apply: Fill the grid with digits 1 to 9 appearing once each in every row, column, and 3x3 box.
Modifying Loop: Draw a single 1-cell-wide loop of orthogonally connected cells into the grid. The loop must fulfill the following rules:
- Different loop segments cannot touch, not even diagonally.
- Each set of three adjacent cells along the loop must consist of exactly one "Incrementer", one "Decrementer", and one "Nullifier" cell.
Killer cages: The values of all caged cells must sum to the small number given. Note: the cages in boxes 1, 6, and 7 each add up to either 20 or 25. Their sum can be different or the same, and must be determined by the solver.
Kropki dots: Cells connected by a white dot contain consecutive values.
Modifiers: For a cage sum, a Kropki comparison, or a Magic Square sum, digits in a "Incrementer" are increased by 1, digits in a "Decrementer" are decreased by 1, and digits in a "Nullifier" are counting as 0.
---- LINKS ----
Solve this puzzle in the CtC app
Solve this puzzle on f-puzzles.com
This Sudoku is part of my series of "build-your-own-loop Sudokus". If you liked solving this puzzle or if you prefer other combinations of loop logic and constraints, feel free to give the other sudokus of the series a go too:
| Loop Logic | Loop Constraint | Further Constraints | ||
|---|---|---|---|---|
| Entropic-Zipper- Loop |
Counting Cells | Entropic Line | Zipper Lines X-clues |
|
| Hiking-through- the-Fog Loop |
Signposts | Dutch Whisper, Polarity Line |
Kropki Dots X-clues |
|
| Renbanimo Loop | Pentominos Guiding Cells |
Renbanimos | Kropki Dots Odd cells |
|
| Deceiving Loop | Wrogn Clues | Wrogn Clues | 9 different constraints |
|
| Count-the- Whispers Loop |
Counting Cells | German Whispers | Kropki Dot | |
| Whisper-me- Sum-thing Loop |
Line-sums | German Whispers | Kropki Dots | |
| Road Running Loop |
Road Runner | Parity Line | Kropki Dots | |
| Magically Modifying Loop |
- | Incrementers, Decrementers, Nullifiers |
Magic Squares, Killer cages, Kropki Dots |
|
| Skiing Loop | Gates | German Whispers | Kropki Dot, Between Lines |
|
| Behaving Loop | 3x3 boxes | Polarity Line | Kropki Dots | |
| Magical Loop | Guiding cells | Modular Line | Magic Squares | |
| Foggy Loop | Guiding cells | Parity Line | Fog of War, Killer Cages |
|
| 10-Suȵ Loop | Moon-or-Sun | 10-Line | Killer Cages | |
| Counting Loop | Galaxies | Counting Line | Killer Cages, Kropki Dots, Quadruple Clues |
|
| Shining Loop | Moon-or-Sun | Parity Line | Killer Cages | |
| Interfering Loops | Slitherlink + Masyu |
Entropic Line + Parity Line |
Killer Cages | |
| Slithering Loop | Slitherlink | Entropic Line | Killer Cages, Little Killer |
|
| BigBang Loop | Galaxies | Parity Line | Row/Column Indexer, Kropki Dots |
|
| Summing Loop | Star Battle | Region Sum Line | Killer Cages, Skyscraper, Kropki Dots |
|
| Whispering Loop | Star Battle | German Whispers | Sandwich Sum |
Solution code: Column 8, followed by row 8
Comments
on 7. July 2024, 05:23 by virus_dave
By far, the hardest of your loop puzzles (but i'm still working on the "Whisper me Sum-thing" one). Absolutely amazing that this solves as-is. Brutal but very unique break-in, and each insight needed seems very original. I can't imagine how you thought of doing this ruleset.
Hopefully not a spoiler: The bit at the end with the "1" was really really cute, too ;)
Absolutely beautiful puzzle. I'm so glad to have solved it. Thank you, @ElChiglia!!
on 10. March 2024, 23:10 by sorryimLate
After practice-solving all your other loops, I finally decided to grab this beast :) It's magical and very hard. I'm not absolutely sure my proof of uniqueness regarding the break-in was unquestionable but after 3 hours I was happy to move on and the rest was not so bad. Definitely had to try multiple options. It would be interesting to see the intended proof path. Thanks for setting, Loop-Master!
on 25. November 2023, 17:13 by Bootenks
This is by far your most difficult break-in. It took me a while to figure out how the magic squares could possibly work.
Afterwards it was just amazing and I was proud to have solved it. The deductions after the break-in were cool and sometimes made me smile.
I hope there will be a few more passionated solvers who want to take up the challenge.
