What is the 45 rule in Sudoku?

In standard Sudoku the 45 rule is most useful as a verification tool. If you have filled eight cells in a row, the ninth must equal 45 minus the sum of the other eight. This is another way of saying the missing digit is whatever was not yet placed - But framing it as arithmetic can help catch errors quickly and lock in the final cell of any unit with eight confirmed digits.

The 45 rule is the cornerstone of Killer Sudoku strategy. In Killer every row, column, and 3×3 box still sums to 45, but you work with cage sums instead of given digits. Add up all cage sums entirely contained within a unit. If their total is less than 45, the difference equals the sum of cells crossing the unit boundary - Called innies and outies.

Example: cage sums inside a row add up to 38, and one cell from another cage crosses into the row. That cell must equal 45 - 38 = 7. You know the exact digit without any other deduction.

See the full explanation in the Killer Sudoku 45 rule guide.

The elegance of 45 comes from its mathematical certainty. No matter how a valid Sudoku is constructed, the constraint cannot be broken. Any solution that violates it is wrong. This makes it both a solving tool and an error-checking mechanism at every stage of the puzzle.