Negative Lines Series #1 - 189 Lines (Negative Renban)
(Published on 1. April 2024, 19:32 by Mikemerin)
Here is a document giving some theorems which can help visualize the grid, along with a solve path and explanations, and a SudokuPad/F-Puzzles script to check Renban errors as you solve.
Happy April Fools Day! This puzzle seems to be missing its lines :)
This started as a crazy idea to have lines with a negative restraint being entire puzzle. The following ruleset ends up putting 189 lines "in" the grid which is where the 189 variant comes from.
After choosing Renban and brute-forcing to find a working grid (there aren't many possible) for over a week, this is the result. It's technically solvable with less digits/info but for it to be a fun puzzle this is as minimal as I can make it.
This will definitely be a series. In addition to a 1 star primer puzzle to introduce the ruleset easier, I'm working on a few other variant combinations with negative lines, all staying towards a minimal "miracle" type one that's doable and enjoyable.
---
Normal Sudoku rules apply.
Renban: for numbers 2-8, row N (horizontal) column N (vertical) and box N's cells (both) all have lines N long in the listed orientations. Lines have consecutive digits in any order, can overlap, and all lines (189 total) are given.
I've included an example image below to help visualize this rule.
Kropki: white dots link consecutive cells. Not all are given.
189: Digits in columns 1/8/9 indicate which column 1/8/9 (respectively) appears in that row.
---
Solve in Sudokupad (includes solution) or F-Puzzles
Example Cell
This ruleset is similar to a Kropki puzzle with a negative constraint, where if "all dots are given" and none are in the grid, adjacent cells cannot be consecutive or be in a 2:1 ratio.
Here is an example of all the "missing" lines that would pass through R8C2. This is also in the document link above.
Therefore putting digits 13572468 in R8C1-8 would break the puzzle as there is now a run of 8 consecutive digits in any order.
-----
Solution code: Row 5 (9 digits)
Comments
on 16. April 2024, 03:40 by FischmitFahrrad
Astonishing logic. Unfortunately way beyond my solving-ability...
Spend ~30 min with nearly no process until looking into your solution path. Just following your solution took me more than an hour to understand the logic :)
Got completely stuck with hint 10, showing that r1c2 can't be '3' since that would break r3 (4567 in the remaining cells).
But I don't understand why that necessarily breaks a 3-cell renban...
Isn't 216475398 a totally valid possibility for r3?
—-
Thanks for the nice words! This is definitely a brutal puzzle especially with a new constraint, so definitely feel good about pushing forward so much and trying to solve it!
Keep at it and you’ll feel good once you’ve broken through the puzzle even more, and I would maybe suggest resetting the puzzle to see if those bits of logic stayed with you as they'll help with the rest of the puzzle too! Repetition is always a great learning experience.
Regarding the R3 order you listed, if you fill out a few more cells you'll soon find both R2C3-4 and R2-3C4 being 3/4 combos which break box 2’s Renban. There are other slightly different combinations in R3 that also eventually lead to a similar problem, and others can cause a run of three numbers connecting into R3C7. Basically, you need a 3 to appear in B3 R3 to break up the run of numbers otherwise there will always be a pair somewhere in that box. B2 is the most restrictive location in the entire puzzle so the setup to get there and break through it is delicate but opens up the puzzle even more after.
Let me know how it goes! Good luck and I hope you're able to give it another go.
-MM
