Sudocyclic Groups
(Published on 9. September 2021, 22:42 by SirSchmoopy)
Please let me know if you have any feedback or if you need any additional clarification of the rules.
Links:
- Normal Sudoku rules apply.
- Digits do not repeat along the indicated diagonal.
1. Let a horizontal cycle be defined as follows:
- For a digit A in column X, look to the digit in the Ath Column.
- For this digit B in the Ath column, look to the digit in the Bth column.
- For this digit C in the Bth column, look to the digit in the Cth column...
- Repeat this process until you are back to the digit A (e.g. eventually you will get to column Z which contains X as its digit, and this points back to the Xth column where you started with the digit A).
The horizontal cycle is then (A -> B -> C -> ...->Z)
2. Let a vertical cycle be defined similarly, but progressing vertically along rows rather than horizontally across columns as above.
3. Let the order of a cycle be defined as the number of unique digits appearing in a given horizontal or vertical cycle
n.b. - the 'start' of a cycle is completely arbitrary, and the order of any cycle is identical regardless of the chosen starting cell.
- Green shaded cells have a horizontal cycle with order equal to the digit in that cell.
- Blue cells similarly have a vertical cycle with order equal to the digit in that cell.
- R9C9's digit contains the order of that cell's horizontal AND vertical cycle. (it would be valid either if it were shaded blue or if it was shaded green)
- Digits in cages form a single, complete horizontal or vertical cycle. (e.g. there is a vertical 3-cycle consisting of R3C4,R4C4,and R5C5 in some order).
(Poorly) Illustrated 6x6 Example:
Shaded cells in the below 6x6 are all valid using the above rules. I've illustrated the cycles for R6C1, so you can see the order 3 vertical cycle (R6C1 -> R3C1 -> R4C1) and order 3 horizontal cycle (R6C1-> R6C3 -> R6C5)
Solution code: Row 8 from left to right (e.g. 123456789)
Comments
on 15. February 2022, 05:47 by Jakhob
Great puzzle love the colored cells and how they interact with the diagonal and the cage constraints!
on 16. September 2021, 11:00 by PrimeWeasel
Enjoyed this a lot! More of a 3 star I'd say though!
on 10. September 2021, 23:45 by Morla
Very nice rule set, indeed. Thank you for the puzzle. Because the colours are sort of arbitrary, I kept messing up the orientation, though. You should consider using inner cell arrows or alike for indication; at least that would've helped me.
Sir Schmoopy: That's a great idea! I think i might make another puzzle with this set of rules, and when I do I'll definitely use arrows or something similarly meaningful rather than just color.
on 10. September 2021, 18:22 by SirSchmoopy
You might ask how this is a generalization of a 1-5-9 puzzle.
You can think of a 1-5-9 puzzle as a puzzle where the order of the horizontal cycle of digits in columns 1, 5, and 9 is always exactly 2!
on 10. September 2021, 11:35 by Arashdeep Singh
Very innovative idea. Loved it.
