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Killer sudoku rules

Killer sudoku looks more complicated than it is: a normal sudoku grid, divided into cages with a small sum number. Here you'll read in plain language what the rules are, how to approach a killer as a beginner, and which mistakes to avoid.

What is killer sudoku?

Killer sudoku is the best-known variant of classic sudoku. The 9 by 9 grid is the same, but it is additionally divided into cages: groups of cells with a dotted line around them and a small number in the corner. That number is the sum of the digits in the cage. Often there are few or even no starting digits — the sums are your foothold. It's not heavy arithmetic: adding up to at most 45 is enough, the rest is logical thinking.

The three rules

1. The normal sudoku rules still apply

Every digit from 1 to 9 appears exactly once in each row, each column, and each 3 by 3 box — exactly as in classic sudoku.

2. Every cage adds up to its sum

The digits in a cage together form exactly the number shown in its top-left corner. A two-cell cage with sum 4 can therefore only be 1 and 3.

3. No duplicate digits within a cage

Each digit may appear at most once in a cage. Sum 4 in two cells is therefore never 2 and 2 — that rule eliminates many options, and that is precisely your tool.

How to approach it as a beginner

You don't solve a killer by guessing, but by starting with the cages that allow only one filling. Three tips to get every beginner going:

Start with the extreme sums

Small and large sums have the fewest options. Two cells with sum 3 can only be 1+2, sum 17 only 8+9. Three cells with sum 6 are always 1+2+3, and sum 24 is always 7+8+9. Cages like that fill in (almost) immediately.

Use the rule of 45

Every row, column, and box adds up to 45. If a few cages fit exactly inside one box, you know what the remaining cell must be: 45 minus the sums of those cages. This is the classic killer trick.

Work with the possible combinations

Unsure about a cage? Think about which combinations the sum allows and check what the row, column, and box already rule out. Often only one option remains — and the puzzle closes in step by step.

Common mistakes

Duplicate digits in a cage

The most common mistake: filling sum 8 in two cells as 4 and 4. Remember that every cage consists of different digits — the error check on BreinPlezier will point it out.

Looking only at the sums

The cages are an extra layer, not a replacement. If you forget rows, columns, and boxes, you'll get stuck. The power lies in combining both.

Committing to a digit too early

If a combination fits a cage in two ways, don't lock it in yet. First find a row or box that rules one of them out — a good killer always offers such a foothold.

Ready to try?

On BreinPlezier you choose from four levels: Easy gives you starting digits as a stepping stone, on Expert the grid starts almost empty. Every puzzle is guaranteed to have exactly one solution, and hints and error checking are ready when you get stuck.

Frequently asked questions about the rules

What does the small number in a cage mean?

That is the sum: the digits in that cage add up to exactly that number. It always sits in the first cell of the cage, top-left.

Can a cage cross the edge of a box?

Yes. Cages ignore box boundaries — they can span two boxes or even rows and columns. Only the cage rules themselves (the sum and no duplicate digits) apply within the cage.

What exactly is the rule of 45?

The digits 1 through 9 add up to 45, so every row, column, and box adds up to 45. By subtracting cage sums from that, you calculate what the remaining cells must be.

How do I start when there are no starting digits at all?

Look for the cages with an extreme sum: two cells with sum 3, 4, 16, or 17, or three cells with sum 6, 7, 23, or 24. Those have only one or two possible combinations — that's where the puzzle starts to unfold.

Does every killer sudoku have just one solution?

A good one does. On BreinPlezier every puzzle is checked before you see it: it is proven to have exactly one solution, at every level.

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