Mod3 line maze
(Published on 3. November 2021, 22:39 by FinnishGuy)
Mod3 line maze
This puzzle is my first take on a new ruleset, involving a construct of mod3 lines. I believe this puzzle should be of medium difficulty. I would appreciate any feedback on whether you find the rule set interesting.
Rules:
1. Standard: Normal sudoku rules apply.
2. Standard little killer: Clues outside the grid give the totals for the indicated diagonals.
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.
5. 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.
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 2. 18 digits, no spaces or commas (e.g. 123456789123456789)
Comments
on 1. July 2023, 09:08 by Taikatalvy
I consider this puzzle (and related) as part of the Sudoku Hall of Fame and History. I feel happy i solved it, very nice and fluent.
on 1. December 2021, 18:57 by DomL
This was a wonderful puzzle. The combination of mod3 and Black Kropki Dots made me think about remainders and mod3 in ways I had never really though about.
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@DomL - Thank you, glad you enjoyed it. The relationship between the black dots and the mod3 line was a bit of a surprise also for me, discovered through the process of setting this puzzle.
on 14. November 2021, 13:08 by ScatterBrain
I tried your harder Mod3 first. By comparison, this was a breeze!
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@ScatterBrain - thanks for solving both. This one was created to showcase the rule and allow people to become familiar with how the mod3 line behaves, while not being too difficult.
There is a third one in the series - "Gone Fishing", which is now scheduled to be activated on December 10 on this site. (Actually this was released on Dec 3)
on 11. November 2021, 15:46 by uvo_mod
Labels angepasst.
on 4. November 2021, 01:15 by Elliott810
Very nice puzzle! Definitely a rule set with much potential. Thx:)
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Thanks @Elliott810 - glad you liked it.
on 3. November 2021, 23:41 by mathpesto
I loved solving this! Very elegant and never a dull moment. I'd love to see more puzzles involving modular arithmetic!
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Thanks @mathpesto!
Yes - modular arithmetic is in the centerpiece of this rule. I have already created a draft of a more complex puzzle, which I will release after some testing.
