Killer Sudoku Solver
Sudoku meets arithmetic — cells are grouped into cages that must sum to the target number shown, with no repeated digits inside any cage.
About Killer Sudoku
Killer Sudoku combines the logic of standard Sudoku with the arithmetic of Kakuro. The 9×9 grid is divided into colored "cages" — groups of adjacent cells. The small number in the top-left corner of each cage is the target sum: all digits in that cage must add up to it, and no digit may appear more than once within the same cage.
Unlike standard Sudoku, Killer Sudoku has no pre-filled given cells — all information comes from the cage sums. This makes it both harder and more elegant. The solver uses backtracking with cage-sum pruning: it rejects any partial assignment where a cage's partial sum already exceeds the target or where the remaining cells can't possibly complete the sum.
Frequently Asked Questions
What is a "cage" in Killer Sudoku?
A cage is a group of adjacent cells outlined with a dashed border. The small number shows the required sum of all digits in the cage. Digits may not repeat within a cage.
Can a digit repeat in a cage?
No. Even if the row, column, and box rules would allow it, no digit may appear twice inside the same cage.
How is Killer Sudoku different from standard Sudoku?
Killer Sudoku has no pre-filled cells. Instead, cage sums provide all the constraints. The rows, columns, and 3×3 boxes still must contain 1–9 each.
How does the solver work?
The solver uses constraint-guided backtracking: it tries each digit in each empty cell, immediately rejecting placements that violate the row, column, box, or cage-sum constraints.
How to Play Killer Sudoku
1 Rules
- ✓ Fill every row with 1–9, no repeats.
- ✓ Fill every column with 1–9, no repeats.
- ✓ Fill every 3×3 box with 1–9, no repeats.
- ✓ Digits in each colored cage must sum to the cage's number.
- ✓ No digit repeats within a cage.
2 Strategies
- 💡 Cage Combinations: List all digit sets that sum to the cage target with no repeats.
- 💡 Innies & Outies: Use the fact that each row/col/box sums to 45 to find hidden values.
- 💡 Elimination: Cross-reference cage constraints with row/col/box constraints.
Tip: A 2-cell cage summing to 3 can only be {1,2}. A 2-cell cage summing to 17 can only be {8,9}. Use extreme cage sums as starting points.