Normal Sudoku rules apply, each puzzle says. What does that mean?
Every row, every column, and every 3x3 box contains the digits 1 to 9 once each.
Those are the rules of sudoku. 81 cells, 81 digits.
You can get really far into this puzzle without relying on the negative constraint, perhaps just long enough to forget it’s there.
Just ignore the title as you solve the puzzle. It wouldn’t be fair to use the title as part of a logical deduction. You shouldn’t need it anyway.
I’ve heard that good fences make good neighbors, so I’ve put a small (virtual) fence between every orthogonally-connected pair of cells.
It is admittedly harder to explain how Sudoku doesn’t actually have anything to do with arithmetic when there are variants like this one which do. And this one has a lot of arithmetic.
In Japan the puzzles (not this one) are “Samunamupure” but a UK newspaper decided adding arithmetic to Sudoku made it a “killer,” and the “Killer Sudoku” name stuck. We call them “Killer Cages” three decades later. No cages in this puzzle, but each tiny arrow defines a “virtual cage,” so it’s a “Little Killer” puzzle. I don’t choose the names!
The key strategy to Region Sum Lines involves lines that are a single cell in one region but three cells in another region. Three and one at the same time. So here’s a puzzle with nine such lines!
Plenty of blue Region Sum Lines all around, plus one of each digit. In case you need a reminder of the digits one through nine!
Given digits can be friends! Who needs lines or dots or cages when you have great big digits? Well, great big digits and a global constraint.
Sometimes a puzzle is less about what goes where, and more about what doesn’t go there.
The rain is gone! I can see all obstacles in my way. Gone are the dark clouds that had me blind. It’s going to be a bright, bright Sudoku day.