Killer Sudoku

Killer Sudoku (also known as Sum Sudoku) combines elements of Sudoku and Kakuro. Like standard Sudoku, the player must fill a 9x9 grid so that each row, column, and 3x3 box contains the digits 1-9. However, instead of pre-filled numbers as clues, the grid is divided into "cages" — groups of cells outlined by dotted lines — each with a target sum. The digits within a cage must add up to the target, and no digit may repeat within a cage.

Rules

1. Fill the 9x9 grid with digits 1-9.
2. No digit repeats in any row, column, or 3x3 box (standard Sudoku rules).
3. The grid is divided into cages marked with dotted borders and a small sum.
4. Digits within each cage must add up to the cage's target sum.
5. No digit may repeat within a cage.
6. The puzzle starts with no pre-filled digits — all information comes from the cages.

Strategies

• Cage Sum Combinations: For a cage of size N with sum S, list all possible combinations. For example, a 2-cell cage summing to 3 can only be {1,2}. A 2-cell cage summing to 17 can only be {8,9}.
• Rule of 45: Each row, column, and 3x3 box sums to 45 (1+2+...+9=45). If all but one cage in a row falls entirely within that row, you can calculate the missing cage's contribution.
• Innies and Outies: When a cage partially overlaps a row, column, or box, the Rule of 45 can determine the value of cells inside or outside the overlap.
• Cage/Row Interaction: If a cage is entirely within one row, its digits are excluded from other positions in that row.
• Naked/Hidden Singles: Same as in standard Sudoku, once candidates are narrowed by cage constraints.

Common Cage Combinations

| Cells | Sum | Combinations |

|-------|-----|-------------|

| 2 | 3 | {1,2} |

| 2 | 4 | {1,3} |

| 2 | 16 | {7,9} |

| 2 | 17 | {8,9} |

| 3 | 6 | {1,2,3} |

| 3 | 7 | {1,2,4} |

| 3 | 23 | {6,8,9} |

| 3 | 24 | {7,8,9} |

Killer Sudoku was invented in Japan, where it first appeared in puzzle magazines in the mid-2000s. The puzzle is believed to have been created by combining the cage-sum mechanic from Kakuro with the grid constraints of Sudoku.

The puzzle gained international recognition when The Times of London began publishing Killer Sudoku in 2005, during the height of the worldwide Sudoku craze. It was marketed as a harder alternative for players who had mastered standard Sudoku.

Japanese puzzle publisher Nikoli played a significant role in developing and popularizing the format, originally calling it "Samunamupure" (Sum Number Place). The English name "Killer Sudoku" was coined by The Times, suggesting it was a more challenging "killer" variant of the standard puzzle.

The format has since become one of the most popular Sudoku variants, appearing in puzzle magazines, newspapers, and apps worldwide. World Puzzle Championship competitions regularly include Killer Sudoku in their lineup of puzzle types.