Zones of Influence
(Published on 6. October 2025, 06:55 by Justalilguy)
Thanks to henrypijames. for help with the wording of the ruleset.
Play online in Sudokupad.
Rules
- Place digits 1-9 in every row, column and box without repeats.
- S-Cell Pair: Each row, column and box has one S-Cell (with 2 digits in it) and as a consequence one empty cell as well. For each S-cell there's a corresponding projection cell which is exactly two cells away (moving straight orthogonally or diagonally) from the S-cell, and whose digit equals the sum of the two digits in the S-cell, with no two S-cells sharing the same projection cell.
- A projection cell cannot touch an S-cell, not even diagonally. Squares are S-cells. Circles are not S-cells.
- Value of an S-cell and the surrounding (upto 8) non-S-cells is double the digit(s). Every other cell's value is it's own digit. Empty cell's value is zero.
- Every box and every line segment isolated by dot(s) has a value that is divisible by 3.
- Black dots connect two cells, where one's digit (or sum of two) is double the other's digit (or sum of two). Not all black dots may be given.
Here's an example of how the projection cells work. Diamonds are projection cells and squares are S-Cells.
Solution code: Box 4 digits in reading order, - for empty cell and smaller digit first for the S-cell
Comments
on 12. October 2025, 18:37 by Justalilguy
Fixed example grid
on 9. October 2025, 06:51 by apothycus
Took a while just to figure out how to annotate the logic effectively! Sooo easy to make mistaken deductions in this one even when being careful! I found keeping track of the potential "zones of influence" around S-cell candidates and liberal pencilmarking to be necessary to find the quite interesting deductions hidden within.
-I would simplify the rules a little by saying "Place a digit 0-9..." and "S-cells don't contain a zero" instead of saying "empty cells" (also avoid the question of "is an empty cell really divisible by something?")
-there's a mistake in the example grid: the diamond in box 3 is wrong
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Thank you for solving! I debated just having 0 instead of empty cell but then the rule about not having 0 in S-cell would be a bit strange and I wanted to avoid having too many number specific rules. Also the example is corrected, thanks!
on 8. October 2025, 01:46 by zeniko
This is an interesting ruleset for a very hatd puzzle. I struggled in particular with what rules considered digits (Kropki, Projection) and what rules considered values (Divisibility) and repeatedly confused the two. In the end, this is still quite a rewarding challenge. Thanks for sharing.
on 6. October 2025, 10:01 by Gilliatt
For non-S-cells surrounding an S-cell, should I double its digit when considering black dots? I wanna make sure because you are not using "value" when describing black dots.
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No, black dots consider digits not values
