Chaotic 3D Full Rank
(Published on 23. August 2025, 09:03 by SparkNights)
Recently when I was watching the video about the solution path of another full rank puzzle, I came up with this idea -- 54-Full rank combining chaos construction and full rank. Later due to the 3rd dimension (region) it has been renamed to "3D Full rank"
Chaos Construction:
Divide the grid into 9 regions. All regions are one-cell wide and nine-cells long, orthogonally connected snakes. No T-shaped tetraomino (branch) or O-shaped tetraomino (2x2 area) may entirely be in a single region. Place the digits 1~9 once each in each row, column, and region. Region borders are partly given.
3D Full Rank:
All rows, columns and regions are regarded as 54 9-digit numbers in total read from both directions. All 9-digit numbers cannot repeat.
Ranking the 54 numbers from the lowest (1) to the highest (54), a clue outside the grid represent the ranking of the 9-digit number in that row/column read from the clued side to the other side. A clue in the top left corner of a cell in the grid indicates the ranking of the 9-digit number in that region read from clued end to the other end.
All cells with a clue, including '?', must be at an end of a region (ie. only 1 of 4 orthogonally neighboring cell is in the same region). To clarify, a '?' represents any number from 1 to 54, not necessarily be a single-digit number.
Solution code: Column 4 (Downwards) with "-" as region borders (eg. 12-34-567-89)
Comments
on 26. August 2025, 21:43 by SparkNights
update puzzle link
on 25. August 2025, 10:00 by Justalilguy
I am shocked at how well this fits together and how well it flows! So much fun, genuinely a masterpiece.
on 23. August 2025, 20:30 by henrypijames
4¼ difficulty. The FR part is almost a red herring - the puzzle is mostly about region geometry, with a pinch of FR sprinkled on. I played on the version with draft area but ended up not needing it even once.
on 23. August 2025, 20:30 by aqjhs
54/54 would recommend!
on 23. August 2025, 18:58 by henrypijames
The rules don't specify whether "?" stands for any number or only a singl-digit number.
--The 4x9 draft version is earlier made, yes it's any number. If necessary I might update the 4x9 draft version.
on 23. August 2025, 10:40 by steeto
Good idea.
on 23. August 2025, 09:04 by SparkNights
Due to clue 3 was misplaced in the previous version, it was deleted and I published a corrected one
