Killer sudoku rules

The basics

Killer sudoku uses the same 9x9 grid as standard sudoku, divided into nine 3x3 boxes. The placement rules are identical: every row, column, and 3x3 box must contain the digits 1 through 9 exactly once.

The difference is cages. The grid is subdivided into groups of cells (usually 2 to 5 cells each) outlined with dashed borders. Each cage has a small number in its top-left corner — the target sum. The digits you place inside that cage must add up to the target, and no digit can repeat within the cage.

Most killer sudoku puzzles give you zero pre-filled digits. The cage sums are all you get.

Rules at a glance

1. Fill every cell with a digit from 1 to 9.
2. Each row contains 1–9 exactly once.
3. Each column contains 1–9 exactly once.
4. Each 3x3 box contains 1–9 exactly once.
5. Digits in each cage sum to the target number shown.
6. No digit repeats within a cage.

Rules 1 through 4 are standard sudoku. Rules 5 and 6 are the killer sudoku additions.

How it differs from standard sudoku

In standard sudoku, you start with 20 to 35 digits already placed and work out the rest using placement logic. There's no arithmetic involved.

In killer sudoku, you typically start with a blank grid. The cage sums replace the given digits as your starting information. You need both placement logic (standard sudoku techniques) and arithmetic (cage sums, combination counting) to solve.

The arithmetic is simple — you're adding single digits and comparing to a target. Most of the work is still logical deduction. The cage constraints actually provide more information than given digits in many cases, which is why killer sudoku can work with zero starting digits.

The 45 rule

The digits 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. Since every row, column, and 3x3 box must contain each digit exactly once, each of these units sums to 45.

This is useful when most cages within a unit (row, column, or box) are fully contained inside that unit. Add up the cage sums of the contained cages and subtract from 45. The result is the sum of any leftover cells — cells from cages that extend across the unit boundary.

If only one cell is left over, you know its exact value. If two cells are left, you know their sum, which limits what they can be. This technique provides information that you can't get any other way. It's the signature tool of killer sudoku.

Getting started: a walkthrough

Step 1: Scan for forced cages. Look for 2-cell cages with extreme sums. Sum 3 can only be 1+2. Sum 17 can only be 8+9. These are free placements. You still need to figure out which cell gets which digit, but you know the options.

Step 2: Apply the 45 rule. Check each row and box. If the cages within a row are mostly self-contained, the 45 rule might hand you a value for free.

Step 3: List combinations for unsolved cages. For each cage, write down every valid combination. A 3-cell cage with sum 10 could be 1+2+7, 1+3+6, 1+4+5, 2+3+5. Cross out any combination that includes a digit already placed in the same row, column, or box.

Step 4: Look for singles. After eliminating combinations, check whether any cell has only one possible digit. That's a naked single — fill it in and continue.

Step 5: Repeat. Each placement gives you new information. Re-check cage combinations, re-apply the 45 rule, and look for new singles until the grid is complete.

Common mistakes

Repeating a digit in a cage. This is the most common error for anyone coming from standard sudoku. Even if two cells are in different rows and columns, they can't share a digit if they're in the same cage.

Forgetting standard sudoku rules. The cage constraints are new and feel like the main challenge, but the row/column/box rules eliminate just as many candidates. Don't ignore them.

Not using the 45 rule. Beginners often try to solve everything from cage combinations alone. The 45 rule gives you information that combination analysis can't, especially for hard puzzles with large cages.

Frequently asked questions