Killer Sudoku rules and puzzles

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