Abstruse
(Published on 28. September 2024, 23:11 by Andrewsarchus)
Rules:
- Normal Sudoku rules apply.
- Draw a one-cell wide loop which does not touch itself (not even diagonally).
- A Home Cell is a cell whose digit is equal to its cell position within its box.
In this puzzle, Home Cells count Loop Cells and Circles count Home Cells - Circles count the number of Home Cells (including themselves if applicable) in
the surrounding 3x3 neighborhood.
All possible circles are given. - Home Cells count the number of Loop Cells (including themselves if applicable) in the surrounding 3x3 neighborhood.
- Only Home Cells are allowed to count Loop Cells,
and Furthermore, any cell whose cell position matches the number of neighboring Loop Cells MUST be a Home Cell.
For example:
if a cell in position 4 sees exactly 4 Loop Cells, then it must contain the digit 4.
In other words, for EVERY cell in the grid...
- Let P = the cell's position within its box
- Let V = the value of the cell (i.e. its digit)
- Let N = the number of Loop Cells it sees in its 3x3 neighborhood (including itself if applicable).
Then either P, V, and N are All Equal OR All Distinct. - White Dots separate consecutive digits.
Not all white dots are necessarily given. - Note: in this puzzle, there is no restriction preventing the overlap of any combination of Circles, Loop Cells, and Home Cells. It is permissible for a cell to be all three.
Play Online:
sudokupad: Abstruse
Solution code: Row 2
(left to right, no spaces)
Comments
on 30. December 2024, 21:23 by 3good5you
Crazy that this puzzle exists, and crazier still that it's so clean to solve (once you internalize the rules)!
on 23. December 2024, 19:14 by askaksaksask
The first challenge for me was internalizing the circle-home-loop interactions and negative constraints. The second challenge was constantly minding these negative constraints throughout the solve. I think a high 4* (>4.5) or 5* might be in order here?
Either way, now the praise: staring at my finished grid, it's kind of a miracle so few clues solve a unique puzzle under these constraints. I think this is truly genius. I really can't believe it. But that's what makes this puzzle so great. Difficulty aside, i hope more people pile in to attempt this because it really is top notch, certainly one of the finest loop entries in 2024.
on 22. December 2024, 20:20 by Myxo
Madness.
on 20. December 2024, 15:51 by Qodec
You wouldn't think this ruleset to be that restrictive, and then the puzzle gradually reveals that it is.
I'll probably spend the weekend wondering how one would have the idea in the first place ('I've got it, I'll do a meta sweeper indexed loop puzzle with a negative constraint on all levels!') but I'm very happy that you did. Awesome puzzle.
on 12. November 2024, 00:14 by Andrewsarchus
Increased difficulty rating
on 18. October 2024, 15:18 by sorryimLate
Very interesting, and amazing that this has a unique solution. But it felt much harder than 3* because it's a new ruleset, at least for me. It's quite challenging to first internalize the rules and then keep in mind all the consequences. Maybe an easier introduction puzzle would bring more solvers? Great construction, thanks!
