The case notes
Use the rule of 45 in a Killer row
Every Sudoku row totals 45. Subtract complete Killer cages inside a row to find its uncovered cell, with a short worked example.
Why the total is 45
Each standard Sudoku row, column and box contains 1 through 9 exactly once. Those digits add up to 45.
Subtract the covered cells
In this example, four cages lie entirely inside the first row and cover eight of its cells. Their clues are 3, 7, 11 and 15, which add to 36. The uncovered cell is 45 minus 36, so it is 9.
Check the cage boundaries
Only subtract a whole cage when all its cells are inside the row, column or box you are counting. A cage that crosses the boundary needs its outside cells accounted for too.
Read the transcript
Every Sudoku row contains one through nine. Add them and you get forty-five. That total can solve a Killer cell without naming the other eight digits. These four cages stay entirely inside the top row. Their clues are three, seven, eleven and fifteen. Together, they account for thirty-six. There is just one row cell left outside those cages. The row needs forty-five, and the cages supply thirty-six. The gap is nine. So this last cell is nine. Look for a row, column or box almost covered by complete cages; its missing total may tell you what remains.
Keep following the clues
- Killer Sudoku rules: cage sums and no repeated digits →
- Killer Sudoku cage combinations: find the digits in a small cage →
- Killer Sudoku: Find an outie from a Killer box →
- Killer Sudoku: add cage sums to find a shared digit set →
- Killer Sudoku: Use a box to constrain a crossing Killer cage →
- Killer Sudoku: Compare two Killer cages through their shared row →
- Killer Sudoku: Let a Killer cage rule out digits nearby →
- Killer Sudoku: Use a sum you worked out as an invisible cage →
- Killer Sudoku: Use a modular line to choose a Killer cage pair →
- Killer Sudoku: Find two missing cells with the rule of 45 →
- Arrow Sudoku: Subtract an overlapping cage from an arrow →
- Arrow Sudoku: Use the rule of 45 to find an arrow circle →