数独中的45法则是什么？

在standard Sudoku中，45 rule最有用的是作为verification tool。如果你已经填满了一个row中的八个cells，第九个必须等于45减去其他八个的和。这是另一种说法，missing digit是尚未放置的数字 - 但将其框架为arithmetic可以帮助快速发现errors并锁定任何有八个confirmed digits的unit的final cell。

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.