How to Play Killer Sudoku

Killer sudoku is sudoku with arithmetic clues. You fill a 9x9 grid so that every row, column and 3x3 box holds the digits 1 to 9 once, and every outlined group of cells (a cage) adds up to the small number printed in it. This guide is for beginners: after reading it you can state the rules, read a killer board and make your first moves.

The rules

1. Fill every cell with a digit from 1 to 9.
2. Each row contains 1 to 9 exactly once.
3. Each column contains 1 to 9 exactly once.
4. Each 3x3 box contains 1 to 9 exactly once.
5. The grid is divided into cages, groups of neighbouring cells. Each cage shows one sum.
6. The digits in a cage must add up to its sum.
7. A digit cannot repeat inside a cage, even when the cells are not in the same row, column or box.

Rules 1 to 4 are classic sudoku. Rules 5 to 7 are what killer adds. Every cell belongs to exactly one cage, so the cage sums together always total 405 (nine boxes of 45). In the example puzzle below, all 24 cage sums add up to 405.

Classic sudoku vs killer sudoku

The last row is a fact about our own catalogue: at Expert and above, the cages alone fix the solution, so you never start with a placed digit. Difficulty follows the same bands as classic sudoku (Easy, Medium, Hard, Expert, Master, Legendary), based on the hardest step a solver needs.

How cages look on our board

On sudoku69 each cage is drawn as a dashed outline around its cells. The sum sits in the top-left corner of the cage, in its first cell. Read the number, count the cells inside the dashed line, and you have everything the cage says. Cell references in this guide use R4C1 for row 4, column 1.

First moves

You do not need candidates yet. Start with two ideas that read straight off the board.

1. Cages with only one combination

Some sums can be made in exactly one way. A two-cell cage of 17 must be 8 and 9, because no other pair of different digits reaches 17. A two-cell cage of 3 must be 1 and 2. The forced sums are:

The full list, including bigger cages, is in the combinations chart, and cage combinations shows how to use it.

2. The 45 rule

Every row, column and box adds up to 45 (1 + 2 + ... + 9). If some cages sit completely inside one house, subtract their sums from 45 to learn about the cells left over.

A small example

This row is one of our own killer Easy puzzles, checked against its stored solution. Numbers are the cage sums; cell positions are given as row and column.

A forced 17. The cage of sum 17 covers R4C1 and R5C1, in the same column and box. Its digits must be 8 and 9. R4C1 is already given as 8, so R5C1 is 9. No solving pattern needed.

The 45 rule on box 1. Box 1 (rows 1 to 3, columns 1 to 3) has two cages fully inside it:

• the 21 cage on R2C1, R3C1, R3C2 and R3C3
• the 6 cage on R2C2 and R2C3

That is 21 + 6 = 27. The box must total 45, so the three remaining cells R1C1, R1C2 and R1C3 add up to 18. Those three cells belong to a cage of 25 that also includes R1C4. So R1C4 = 25 - 18 = 7. A cell that sticks out of a region like this is an innie; the technique has its own article, innies and outies.

Both results match the puzzle's solution (R5C1 = 9, R1C4 = 7).

What to do after the first moves

1. Mark the digits each forced cage can hold, then remove them from the rest of the row, column or box when the cage sits in one.
2. Work out the 45 total for each box, row and column against the cages inside it.
3. Fill in candidates only when the arithmetic runs out.
4. Check every cage for repeats before you commit a digit.

Common slips: assuming a cage has the digits in a set order (the sum tells you the set, not the order), and forgetting that a cage may not repeat a digit even when it bends across two boxes.

Where to play

Start with Easy killer sudoku, where forced cages and the 45 rule are enough to make progress. The killer sudoku and math variants overview puts killer next to other arithmetic puzzles.