Killer Sudoku Solver,
cages in, finished grid out.

Field guide

How the Killer Sudoku Solver works.

Killer Sudoku keeps every rule of the classic puzzle: each row, column and 3×3 box holds the digits 1 to 9 once. What changes is the set of clues. Instead of starting digits, the grid is divided into outlined cages, and each cage carries a small total in its corner. The digits inside a cage must all be different and must add up to that total. Because those totals are the only clues, a good killer puzzle is as much arithmetic as logic.

Entering your puzzle

Stay in Draw cages mode, tap each cell of one cage on the board, type the cage's sum and press Add cage. The cage appears with a dashed outline and its sum in the corner, just like the printed puzzle. A tint separates neighbouring cages, and tapping a finished cage lets you change its sum or delete it. If your puzzle does show a few starting digits, switch to Enter given digits. The status line watches for slips: a complete grid must total 405, a cage cannot hold an impossible sum, and an uncaged cell is flagged. The Example button loads a practice puzzle written for this tool.

Cage combinations

Every cage is a small puzzle on its own: which different digits can add up to the total? A cage of n cells can only reach sums within a fixed range.

Two cells can reach 3 to 17, three cells 6 to 24. Totals at the edge of a range have only one answer: two cells adding to 17 must be 8 and 9, and three cells adding to 7 must be 1, 2 and 4. A total one step inside, such as three cells adding to 8, allows two sets, 1 + 2 + 5 or 1 + 3 + 4. The calculator above the guide lists these sets for any size and sum, and lets you require or rule out digits as you learn more about the grid.

The 45 rule, worked through

Each row, column and box adds to 45, which gives the solver extra clues that are not printed. Suppose three cages lie entirely inside one row and their sums are 9, 16 and 11. Together they use 36, so the two remaining cells of that row must add to 9. Cells that poke out of a unit work the same way once the whole unit is caged. The solver adds these implied cages automatically.

What happens when you press Solve

The solver keeps a list of possible digits for every cell. It strips out digits already used by a row, column or box, fills cells that have only one candidate left, and for each cage keeps only digits that appear in a combination still consistent with its cells. When that stops making progress it guesses in the most constrained cell and backtracks if the guess fails. The search runs in a background thread with a limit, so the page never freezes. After finding a grid it also looks for a second one and tells you if your puzzle is not unique, which usually means a misread sum.

Tips for solving by hand

• Start with the extremes. Two cells adding to 3 or 17, three cells adding to 6 or 24, and similar cages have only one digit set.
• Use the 45 rule early. Total the cages inside a row, column or box and see what is left over.
• Cross-check cages with their units. Cages that sit in one row cannot reuse a digit used elsewhere in that row.

Disclaimer: This tool is an independent puzzle aid, not affiliated with any puzzle publisher or app, and is provided for practice and entertainment only. Check the result against your own puzzle before relying on it.