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Killer Sudoku Cage Sums: Totals and the Rule of 45

Use the total and the current unit restrictions together. An original lesson from the verified puzzle collection.

Actual killer-sudoku board with original puzzle clues and controls

The rule

Use ordinary Sudoku units. Every connected cage has the indicated total and contains no repeated digits.

Read the constraint

A two-cell cage totaling 3 contains 1 and 2, in some order. A cage totaling 10 does not make every sum-to-10 pair available: any digit excluded by a row, column or box is unavailable in that cell.

Connect the candidates

The cage assistant shows ordered compatible sequences using the current board. Its cell order is explicit. Filled digits count toward the target, and repeated cage digits are rejected.

Make a justified move

A complete row, column or box totals 45. If fully enclosed cages account for 36, the remaining cells sum to 9. This arithmetic becomes useful only after checking which cages are wholly inside the unit.

A real puzzle example

Open killer-sudoku-001, then focus on r1c1. The explanation below is generated from this puzzle’s logical proof, without looking up its answer.

Reveal the explained next step
  1. These 4 cage cells must total 21, with no repeated digit.
  2. These 2 cage cells must total 11, with no repeated digit.
  3. These 4 cage cells must total 22, with no repeated digit.
  4. These 2 cage cells must total 16, with no repeated digit.
  5. These 3 cage cells must total 19, with no repeated digit.
  6. These 2 cage cells must total 8, with no repeated digit.
  7. These 2 cage cells must total 6, with no repeated digit.
  8. These 2 cage cells must total 7, with no repeated digit.
  9. These 2 cage cells must total 8, with no repeated digit.
  10. These 4 cage cells must total 17, with no repeated digit.
  11. These 4 cage cells must total 17, with no repeated digit.
  12. These 3 cage cells must total 20, with no repeated digit.
  13. These 4 cage cells must total 20, with no repeated digit.
  14. These 2 cage cells must total 8, with no repeated digit.
  15. These 1 cage cells must total 8, with no repeated digit.
  16. These 4 cage cells must total 19, with no repeated digit.
  17. These 4 cage cells must total 20, with no repeated digit.
  18. These 2 cage cells must total 13, with no repeated digit.
  19. These 2 cage cells must total 10, with no repeated digit.
  20. Every other digit is excluded by the current units and constraint candidates.

The justified digit is 3.

Practice without a penalty

Use Notes to record options. Undo restores digits and notes together. Hints reveal attention, explanation and conclusion in separate steps. All 200 puzzles are open. A daily selection is a replay from the verified pool, with its own save.

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