Busy Streets
(Published on 12. November 2021, 18:01 by FinnishGuy)
Busy Streets
This puzzle is based on a new ruleset. If you have not yet done so, I recommend getting familiar with the ruleset through the simpler Mod3 Maze puzzle (available through the link for my other sudokus below).
Rules:
1. Standard: Normal sudoku rules apply.
2. Standard killer: Digits in cages must sum to the small clue in the top left corner of the cage.
3. Kropki without negative constraint: Cells separated by a white dot are consecutive. Cells separated by a black dot have a ratio of 1:2. All possible dots are not given.
4. NEW: Mod3 line: Lines in the grid are mod3 lines.
Each mod3 line has a repeating 3-cell pattern of mod3 residuals of the cells along the line. This means that every third cell along the line is from the same mod3 group:
Group 1 (yellow): 1, 4 and 7, all having a mod3 of 1.
Group 2 (red): 2, 5 and 8, all having a mod3 of 2.
Group 0 (green): 3, 6 and 9, all having a mod3 of 0.
The sequence in which the groups repeat along the lines may differ between lines.
For clarity: Any digit on the line cannot have another digit from the same mod3 group within 2 cells to either direction on the line.
The following are valid examples of mod3 lines:
The following is an example of an invalid mod3 line. The fourth digit along the line (6) should be from the same mod3 group as the first digit (4), but it is not. Valid numbers for the fourth cell would be 1 or 7, or even 4 if the line is arranged in such a way that it would not violate the rules of sudoku.
There are no other restrictions on the lines. Digits may repeat along the mod3 line if allowed by other rules.
I hope you enjoy the puzzle. Feel free to leave comments.
Try also my other Sudoku puzzles
Solution code: Row 3 + column 3, 18 digits, no commas or spaces (e.g. 123456789123456789)
Comments
on 14. November 2021, 12:33 by ScatterBrain
First time I tried Mod3 line. It was a real challenge, and a great idea!
on 13. November 2021, 13:37 by uvo_mod
Labels angepasst.
on 12. November 2021, 21:22 by 10feet
I liked how the mod3 rule and the black Kropki interacted. Thanks.
on 12. November 2021, 18:32 by FinnishGuy
Clarified mod3 rule.
on 12. November 2021, 18:13 by 10feet
Question about Mod3 lines. Are different positions required to be different values mod3? Otherwise, length 3 lines don't seem to add any restriction at all.
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@10feet: I will clarify the rule in the puzzle page. You are correct, the intent is that the line cannot contain a digit from the same Mod3 "family" within 2 cells to either direction. In case of a line of length 3, this means that all 3 cells must be from different "families".
