Behaving Loop
(Published on 11. November 2023, 07:35 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.
Polarity Loop: Draw a single 1-cell-wide loop of orthogonally connected cells into the grid. The loop must fulfill the following rules:
- The loop enters every 3x3 box at least once.
- Different loop segments cannot touch, not even diagonally.
- If a cell contains a square, it cannot be part of the loop. Furthermore, the digit in it counts the total number of cells in the respective 3x3 box that are part of the loop.
- Adjacent digits on the loop must have different polarity, i.e., they must alternate between low (1234) and high (6789).
---- LINKS ----
Solve this puzzle in the CtC app
Solve this puzzle on f-puzzles.com
This is the eleventh Sudoku in 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 11. April 2024, 00:57 by virus_dave
Oh man that first flash of insight needed to make progress... What a brilliant puzzle!
on 7. April 2024, 16:32 by bansalsaab
That breakin is 5*
on 6. February 2024, 04:01 by shteev
Really enjoyed this! Couldn't find the shape of the loop without bifurcating, tho... Even when I understood what was making the incorrect loop break, I couldn't reduce the reasoning to short logical steps
----
Hi, thanks for the feedback. I will reply in a hidden comment why I think that bifurcation is not needed or not the right term to describe what is supposed to be realized :)
-- ElChiglia
on 8. December 2023, 21:46 by NightDog
Beautiful finishing line
on 20. November 2023, 02:04 by heliosfant
Amazing puzzle
on 11. November 2023, 19:38 by Briks
I liked it very much.
No guessing necessary.
