The Enchantments (GW loop Chaos Deconstruction)
(Published on 26. July 2025, 20:55 by SeveNateNine)
Chaos Deconstruction/ Numbered Regions: Fill some cells with a digit from 1-9 such that no digit repeats in any row or column. Divide the filled cells into nine orthogonally connected regions, each containg a set of the digits 1-9 respectively. In the upper-left hand cell (leftmost cell of top row) of each region is a region number, N. This number is different for all regions.
German Whisper Loop: Draw an orthogonally moving loop through non-empty cells which does not touch itself orthogonally, or diagonally, on which adjacent digits differ by at least five.
Circles mark every instance of a region number that is visited by the loop.
Within a region N, the loop must visit exactly N-1 cells. The regions are visited in ascending order (excluding region 1) with region nine connecting to region two.Arrows indicate the number of loop cells in the indicated direction. (Not including the cell itself) Cells with multiple arrows count each direction separately.
Caged cells contain a digit equal to the number of cells seen vertically and horizontally (including itself) within its region. Region borders block sight lines. *ALL CAGES ARE GIVEN*
Much thanks to Andrewsarchus, and Crusader175 for testing!
Solution code: Loop cells in rows 9 and 10.
Comments
on 7. August 2025, 09:29 by TitaniaLowe
This took me three and a half hours to solve and I can't help but feel like I must have missed some really obvious deductions in the last third or so of the puzzle. Anyway, absolutely brilliant!
on 6. August 2025, 14:06 by MagnusJosefsson
Fantastic puzzle, very enjoyable and challenging!
on 5. August 2025, 21:08 by SeveNateNine
Changed sum to count
on 5. August 2025, 20:05 by Phistomefel
I'm very curious about this puzzle, but there is a rule I would like to ask you about. Cells with multiple arrows sum each direction separately. Does this mean that the count of the loop cells in the directions are summed or that every direction sees the same number of loop cells?
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Each direction sees the same number of loop cells.
on 2. August 2025, 21:34 by steveire
I was able to solve it, but it was too difficult for me to enjoy...
on 1. August 2025, 08:51 by SeveNateNine
Clarification
on 1. August 2025, 07:51 by steveire
Are region numbers in the topmost position of the leftmost column, or the leftmost position of the top column?
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It is the leftmost cell of the top row.
on 27. July 2025, 22:05 by marcmees
amazing puzzle. thanks
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Glad you enjoyed!
on 27. July 2025, 10:09 by han233ing
I never imagined these two types of fully given circles and cages would have such a powerful effect.
on 27. July 2025, 08:32 by SeveNateNine
Fixed mistake in solution check.
on 26. July 2025, 21:32 by SeveNateNine
Added missing rule
on 26. July 2025, 21:27 by marcmees
and circles?
on 26. July 2025, 21:05 by Andrewsarchus
I really love this puzzle. Every deduction feels beautiful and brilliant.
