Apophenia (Nuri-uzu/Mid-loop/Clone)
(Published on 5. October 2025, 18:22 by dumediat)
This puzzle was created for round 2 of Agent's Puzzle Agency Contest (PAC) held in the Sudoku Skunkworks Discord server. In this round, participants were tasked with creating a puzzle that uses two 3x3 non-overlapping clones which had to copy two different attributes from numbers, colors, and line segments. I had seen the "Amalgam" ruleset (coined by Shintaro Fushida-Hardy) in the past, and thought the ambiguous grid placements could cause some cool interactions with the known clone locations.
Ratings, comments, and feedback are much appreciated! Please feel free to reach out to me on Discord if you have any comments or questions. Please also feel free to try my other puzzles here.
Rules:
- Amalgam: The 15x15 outer grid contains two overlapping 9x9 inner grids which must be located by the solver. One is a nuri-uzu and the other is a mid-loop. Circles in the overlap are both nuri-uzu clues and mid-loop clues. Circles which are in neither inner grid are ignored. Grid borders may not divide two cells that share a circle.
- Nuri-uzu: Shade some cells such that all unshaded cells form contiguous regions that contain exactly one circle. Unshaded regions must be rotationally symmetric with the circle at its center. Cells overlapping a circle may not be shaded, and there may not be any 2x2 areas that are fully shaded or unshaded. Cells outside the nuri-uzu grid may not be shaded, and are ignored for all nuri-uzu rules.
- Mid-loop (variant): Draw a non-intersecting, non-branching loop through the centers of some orthogonally connected cells that goes through every circle. Each circle marks the center of the straight line segment it lies on.
- Variant rule: The loop may not turn on shaded cells.
- Clones: The two outlined 3x3 areas are clones. All loop segments and shading must be exactly duplicated in every pair of cells in the same relative positions of the clones, without rotation or reflection. Cells that are in neither inner grid are considered unshaded for this purpose.
Penpa+: https://tinyurl.com/24jmc3sv
Solution code: Using the full 15x15 grid, the number of loop turns in each row (top-to-bottom) followed the longest stretch of shaded cells in each column (left-to-right) (30 digits)
Comments
on 17. October 2025, 07:34 by opel
Very fun!
on 10. October 2025, 18:49 by the_cogito
Really liked this, thank you!
on 6. October 2025, 05:10 by Piatato
Very cool puzzle!
on 5. October 2025, 20:48 by damasosos92
Gorgeous, brilliant and not too hard! A masterpiece.
on 5. October 2025, 19:11 by sfushidahardy
The clone logic was super interesting!
on 5. October 2025, 18:50 by Silverbyte
The ruleset sounded nightmare-ish but this was actually really approachable and an absolute blast to solve. Great puzzle!
on 5. October 2025, 18:42 by Christounet
Awesome puzzle. Best one of round 2 for me! The use ofnthe clones is very subtle. Thanks :)
on 5. October 2025, 18:31 by Agent
Awesome puzzle with a really elegant solution path!
