How to Solve Sudoku: Cage Combinations (Killer)

List the combinations of digits that make a cage's sum and rule out those that cannot fit. A digit used by none of the remaining combinations can be removed from that cell.

Also called narrowing down the combinations, in Killer Sudoku. On Puzzle Lounge it appears from Killer Easy up.

See it step by step

  1. Look at the cage with sum 12 (the dotted 2 cells; the number at the top left is the sum)
  2. 12 can be made with 3+9, 4+8 or 5+7 (a different digit in each of the 2 cells)
  3. If it is 1, the other would be 11 (not a digit from 1 to 9, so it is out)
  4. If it is 6, the other would also be 6 (a cage cannot repeat a digit)
  5. If it is 4, the other would be 8 (but row 1, column 6 has no note for 8)
  6. So they can be removed from this cell's notes (1, 4 and 6 go from row 1, column 5, leaving 3, 5, 7, 8 and 9)

This is Killer Easy No.1, partly solved.

Solve this puzzle →Print and solve →

How to find it

  1. Start with the cages with few cells. In the quick table below, look first for sums that have just one combination.
  2. Write out every combination that makes the sum.
  3. Rule out combinations with a digit the cage's other cells cannot hold, then erase from the notes any digit in none of the remaining combinations.

Things to watch

  • A digit cannot be repeated inside a cage (6+6 is not allowed).
  • The combinations depend on the number of cells and the sum. You can also use the quick table on the Killer page.
Read the full explanation

Each dotted cage in Killer shows its sum. List the combinations of digits that make the sum and rule out those that cannot work in the same cage, row, column or box. A digit in none of the remaining combinations cannot go in that cell.

For a 2-cell cage with sum 12, the combinations are 3+9, 4+8 and 5+7: 3 in all (6+6 is out, since it repeats a digit).

If 8 cannot go in the other cell, 4+8 is out. Only 3+9 and 5+7 remain.

So this cell holds one of 3, 5, 7 or 9. Any other notes can be removed.

Row 1, column 5 is in a 2-cell cage with sum 12. The combinations for 12 are 3+9, 4+8 and 5+7. If it is 1, the other would be 11, which is not a digit from 1 to 9, so it is out. If it is 6, the other would also be 6, and a cage cannot repeat a digit. If it is 4, the other would be 8, but row 1, column 6 has no note for 8. So 1, 4 and 6 can be removed from this cell's candidates.

Other techniques

Hidden SingleNaked SinglePointingClaimingHidden PairHidden TripleRule of 45 (Killer)Naked PairNaked TripleX-WingXY-WingSwordfishSkyscraper2-String KiteXYZ-WingW-WingJellyfish

For the basics and how to use notes, see how to solve sudoku, with tips. If you get stuck, the game's hints guide you step by step, starting with where to look.

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