Killer Sudoku rules and puzzles

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