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Killer Sudoku: Rules & How to Solve

Cages with target sums turn classic sudoku into an arithmetic puzzle. Here's the rule and the techniques that crack it.

The rule

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Digits inside a dotted cage must add up to the small number printed in its top-left corner, and a digit can't repeat within a single cage. Normal sudoku rules still apply: 1–9 once per row, column, and box.

How to solve killer sudoku

The 45 rule

Every row, column, and 3×3 box totals 45. If cages cover a box and spill out by one cell, you can solve that cell by subtracting the cage sums from 45.

Lock small cages first

A two-cell cage summing to 3 can only be {1,2}; a sum of 17 can only be {8,9}. These "killer pairs" eliminate candidates from the whole row, column, or box.

No repeats inside a cage

Even when several combinations fit a sum, the no-repeat rule often rules most of them out — a 3-cell cage of 7 is {1,2,4}, never {1,3,3}.

Frequently asked questions

Do digits repeat inside a killer cage?
No. A digit can appear at most once per cage, on top of the usual row, column, and box constraints.
What is the 45 rule in killer sudoku?
Each row, column, and box contains 1–9, which sums to 45. Comparing cage totals against 45 lets you deduce leftover cells.
Is killer sudoku harder than normal sudoku?
It adds an arithmetic layer, but the cage sums also give extra information — many solvers find well-set killers more satisfying than classic grids.

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