Killer Sudoku Solver

Enter the cages and sums of a 9×9 Killer Sudoku to check that it has exactly one answer, see the solution, or reveal one cell at a time with the rule behind it. The 45 rule helper and the sum combination table help when you solve it yourself.

How to use

1. To try the tool first, press "Example, easy" or "Example, medium".
2. In "Cages" mode tap the cells of one cage, type its sum on the keypad and press "Make cage". The cage gets a dotted outline and its sum in the top-left corner. "Unpick" cancels the selection and "Delete cage" removes the cage under the selected cell. If the puzzle has given digits, enter them in "Digits" mode.
3. Read the message under the grid: it names cells without a cage, overlapping cages, sums that cannot be made with different digits and repeated givens.
4. Press "Solve". The answer appears in blue with a message saying whether it is unique. "Hide answer" removes it, and "Hint: one cell" fills one cell in green and explains why.
5. In the "45 rule helper" choose a row, column or box to see the cages that lie entirely inside it and the sum of the remaining cells. "Save as PNG" downloads the grid; "Clear all" empties it.

How it works

• The solver combines the sudoku rule with every cage: it lists the digit sets that still fit each cage, keeps only digits that appear in them, and adds sum constraints from the 45 rule for single rows, columns and boxes and for groups of two or three. When the rules stall it tries values in the cell with the fewest possibilities, keeps searching to check uniqueness, and stops after 10 seconds.
• Hints look for, in order: a one-cell cage, a cell whose row, column and box hold every other digit, a digit with only one place in a house, and a cage whose combinations leave one digit. Then the full narrowing with the 45 rule is used; if even that decides nothing, one cell comes from the solution.
• The board, the answer and the hints are kept in this browser only.

Killer Sudoku rules

As in sudoku, each row, column and 3×3 box holds 1 to 9 once. The grid is also divided into cages drawn with dotted lines. The digits in a cage add up to the small number in its corner, and a digit cannot repeat inside a cage, even when its cells lie in different rows and boxes. Most Killer Sudokus have no given digits at all.

Solving Killer Sudoku by hand

Use the 45 rule. Every row, column and box adds up to 45. If cages lying entirely inside a box add up to 38 and one cell of the box is left over, that cell is 7. If a cage sticks out of a box by one cell, the cage sum minus what the box needs from it gives that outside cell.

Look up cages with a single combination: two cells adding to 3 or 17, three cells adding to 6, 7, 23 or 24, four cells adding to 10, 11, 29 or 30. A three-cell 7 is always 1, 2 and 4. Once a combination is fixed, its digits leave the other cells of any row, column or box the cage lies in.

Questions and answers

What if the solver finds more than one answer?

A published Killer Sudoku has one answer. Several answers usually mean a cage is missing, two cages were merged, or a sum was misread. One possible answer is shown so that you can compare it with the paper.

What is the 45 rule in Killer Sudoku?

The digits 1 to 9 add up to 45, so every row, column and box does too. Subtracting the cages that lie fully inside a house gives the sum of its remaining cells; the helper on this page does this subtraction.

Do all cells need to be in a cage?

In a normal Killer Sudoku, yes. A cell without a cage is accepted only if it has a given digit.

Can a cage repeat a digit?

No. In Killer Sudoku the digits in a cage are all different, which is why the combination table lists sets of different digits.