The case notes
Use a sum you worked out as an invisible cage
These two Killer cages cover six cells of the top row. Three cells sit outside them, and one of those is an eight. Watch a worked example, then try the idea in a puzzle.
Put it into practice
Two cages. Three cells left.
These two Killer cages cover six cells of the top row. Three cells sit outside them, and one of those is an eight.
45 − 8 − 22 = 15
A row totals forty-five. The cages give eight plus twenty-two, which is thirty. So the three uncovered cells must total fifteen.
15 − 8 = 7
One of those cells already holds eight. Take it away from fifteen, and the last two cells must sum to seven. There is no cage drawn around them, but the sum is just as useful.
1+6 · 2+5 · 3+4
Two different positive digits make seven as one and six, two and five, or three and four. Seven itself cannot go in either cell: its partner would need to be zero.
A learned sum works like a cage
The rule of forty-five gave us a new sum. We can use its combinations exactly as we would use a printed cage clue.
Read the transcript
These two Killer cages cover six cells of the top row. Three cells sit outside them, and one of those is an eight. A row totals forty-five. The cages give eight plus twenty-two, which is thirty. So the three uncovered cells must total fifteen. One of those cells already holds eight. Take it away from fifteen, and the last two cells must sum to seven. There is no cage drawn around them, but the sum is just as useful. Two different positive digits make seven as one and six, two and five, or three and four. Seven itself cannot go in either cell: its partner would need to be zero. The rule of forty-five gave us a new sum. We can use its combinations exactly as we would use a printed cage clue.
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 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 →