This killer sudoku solver lets you copy a puzzle from a book or app in a minute: drag across the cells of a cage, type its sum, press Enter, and move to the next one. When every cage is in, press Solve for the full answer or Next hint for one step at a time.
How to draw the cages
- Choose Cages above the grid.
- Drag your finger or mouse across the cells of one cage, or tap them one by one. Tap a selected cell again to drop it.
- Type the sum and press Add cage (or Enter). The cage gets a dashed outline and its sum in the top-left cell.
- To fix a cage, tap one of its cells: you can change the sum or delete it. The counter under the buttons shows how many of the 81 cells are covered.
If your puzzle also prints some digits, switch back to Digits and type them in. The solver checks each sum as you add it: two different digits add up to between 3 and 17, three to between 6 and 24, and so on.
How the solver reasons
The rules are those of sudoku plus two more: the digits in a cage add up to its sum, and no digit repeats inside a cage. The exact search uses both rules to prove the answer is unique. The step-by-step solver adds two killer techniques to the usual sudoku ones:
- Cage combinations. A two-cell cage of 3 can only be 1+2; a three-cell cage of 23 can only be 6+8+9. The solver lists the combinations that fit the candidates and removes digits that appear in none of them.
- The 45 rule (innies and outies). Every row, column and box adds up to 45. If the cages wholly inside a box add up to 38, the remaining cell or cells of that box add up to 7. The same works for two or three neighboring rows or columns (90 and 135), and for the cells of crossing cages that stick out.
After those it uses singles, pairs, pointing, X-wings, wings and coloring, then trial and error only if nothing else applies. Every step in our tests was checked against the true solution.
A worked example
Load the example. The first steps are cage combinations: a two-cell cage of 14 must be 5+9 or 6+8, so 1, 2, 3, 4 and 7 come out of both cells. After about twenty of those the 45 rule appears: the cages wholly inside a row or column add up to a known total, so its remaining cells must make up the rest of 45.
Tips
- Most killer puzzles have no printed digits at all; that is fine, the cages are enough when the puzzle is well made.
- If the solver reports more than one solution, a cage sum is probably mistyped. Compare the highlighted cells with your source.
Cage sums follow the same arithmetic as kakuro: the kakuro combinations chart lists every set of different digits that makes a given sum, which is exactly what a killer cage needs. Cages that also subtract, multiply and divide are the rule in calcudoku.
For a new puzzle every day, play killer sudoku online, with grids made and rated by this solver.
Solver tested . Found a problem? Tell us.
Questions
Can a digit repeat inside a cage?
No. In standard killer sudoku the digits in a cage are all different, as well as following the row, column and box rules. This solver uses that rule.
What is the 45 rule in killer sudoku?
The digits 1 to 9 add up to 45, so every row, column and box sums to 45. Subtracting the cages that sit wholly inside a box gives the total of its remaining cells, which often pins down a digit.
What are the combinations for a cage?
For two cells: 3 = 1+2, 4 = 1+3, 16 = 7+9, 17 = 8+9 are the only ways. For three cells: 6 = 1+2+3, 7 = 1+2+4, 23 = 6+8+9, 24 = 7+8+9. The hint lists every combination that still fits.
Do I have to cover every cell with a cage?
No, but most killer puzzles do. Cells outside any cage simply follow the normal sudoku rules.
Does the solver handle killer puzzles with given digits?
Yes. Switch to Digits and type the printed numbers; they count as clues together with the cages.