KILLER SUDOKU TOOL

Killer Sudoku Combination Calculator

Enter a cage size and target sum to list every legal combination of distinct digits. Exclude digits already ruled out by the row, column, box, or cage.

Find cage combinations

Killer cages use digits 1–9 without repeats. Combinations show which digits can appear, not their order in the cage.

Exclude unavailable digits

Select any digit that cannot appear in this cage.

1 legal combination(s)

  • 8 + 9

Use cage combinations with the 45 rule

A combination narrows the digits in one cage. The 45 rule connects those cage totals to a complete row, column, or 3×3 box.

What a cage combination proves

A two-cell cage totaling 17 must contain 8 and 9. It does not tell you which cell is 8. Use row, column, and box restrictions to determine the order.

  • Digits may not repeat inside one cage.
  • Extreme sums usually have the fewest combinations.
  • Excluding a digit is valid only when another rule has already removed it from every cell in the cage.

How the 45 rule works

Every complete Sudoku row, column, and 3×3 box contains 1 through 9, so its digits total 45. When known cage totals account for a complete region except one cell or a clearly tracked crossing segment, subtract from 45 to find the remainder.

Do not add cage clues blindly when a cage crosses the region boundary. Include or remove the crossing cells explicitly before making the subtraction.

  • Eight accounted cells total 42, so the ninth cell is 3.
  • A box fully covered by cages totaling 45 is balanced but may still need classic Sudoku logic to place each digit.
  • After finding a remainder, verify that it is legal in the cell’s row, column, box, and cage.

Killer combination FAQ

Can a digit repeat inside a Killer Sudoku cage?

No. Every combination produced by this calculator uses distinct digits from 1 through 9.

Does a combination determine digit order?

No. A combination identifies the set of digits in the cage. Row, column, box, and neighboring cage constraints determine their positions.

Why does every row, column, and box total 45?

Each contains the digits 1 through 9 exactly once, and 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 equals 45.

When is the 45 rule unsafe?

It is unsafe when cage clues cross the boundary and their outside cells have not been accounted for. Track every included cell before subtracting.