The case notes
Find two missing cells with the rule of 45
A row always totals forty-five. These three Killer cages cover seven of its cells, leaving two cells outside. Can their clues tell us what those two contain? Watch a worked example, then try the idea in a puzzle.
Put it into practice
A row totals 45
A row always totals forty-five. These three Killer cages cover seven of its cells, leaving two cells outside. Can their clues tell us what those two contain?
3 + 7 + 18 = 28
The cages stay wholly inside this row. Their clues are three, seven and eighteen. Together they cover twenty-eight of the row’s forty-five.
45 − 28 = 17
Forty-five minus twenty-eight is seventeen. So the two uncovered cells must add to seventeen, even though they have no cage clue of their own.
8 + 9 = 17
Only eight and nine, the two largest Sudoku digits, can make seventeen. We have discovered a two-cell sum; now it behaves like a cage without a drawn outline.
Column nine fixes the order
Column nine already has an eight at the bottom. The top cell cannot be eight, so it is nine. The other uncovered cell is eight.
Read the transcript
A row always totals forty-five. These three Killer cages cover seven of its cells, leaving two cells outside. Can their clues tell us what those two contain? The cages stay wholly inside this row. Their clues are three, seven and eighteen. Together they cover twenty-eight of the row’s forty-five. Forty-five minus twenty-eight is seventeen. So the two uncovered cells must add to seventeen, even though they have no cage clue of their own. Only eight and nine, the two largest Sudoku digits, can make seventeen. We have discovered a two-cell sum; now it behaves like a cage without a drawn outline. Column nine already has an eight at the bottom. The top cell cannot be eight, so it is nine. The other uncovered cell is eight.
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 rule of 45: find a missing digit in a row →
- 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 →
- Arrow Sudoku: Subtract an overlapping cage from an arrow →
- Arrow Sudoku: Use the rule of 45 to find an arrow circle →