Rules of Killer Sudoku: How to Play

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Published May 9, 2026 · 16 min read

The rules of Killer Sudoku are simple, but the puzzle feels different from classic Sudoku because the grid usually starts with no given digits. Instead of clues printed in cells, you get outlined groups of cells called cages. Each cage has a small number showing the sum of the digits inside it.

This guide explains the rules clearly, then goes a step further: how to read cage clues, why repeats are normally forbidden, how to make your first deductions, and when to move from pure rules into beginner strategy.

What is Killer Sudoku?

Killer Sudoku is a 9x9 Sudoku variant that combines classic Sudoku logic with arithmetic cage clues. You still fill the grid with digits 1 to 9, and every row, column, and 3x3 box still contains each digit exactly once.

The difference is the clue system. A classic Sudoku gives you starting digits. Killer Sudoku usually gives you an empty grid divided into cages. The cage totals tell you which groups of digits can fit, and the Sudoku rules tell you where those digits can go.

Killer Sudoku is sometimes called Sum Sudoku or Samunamupure. The important idea is that you are not guessing arithmetic answers; you are combining sums with normal Sudoku logic.

The rules of Killer Sudoku

A standard Killer Sudoku puzzle follows five rules. The first three are classic Sudoku rules, and the last two are Killer-specific rules.

Together, these rules mean each cage is both an arithmetic clue and a Sudoku region. A cage sum can narrow the possible digits, while rows, columns, and boxes decide the order.

How Killer Sudoku cages work

A cage is an outlined or coloured group of cells. The small number in the cage, usually shown in the top-left cell, is the total for the whole cage. If a cage says 12 and contains three cells, those three cells must add to 12.

Cage clues do not usually tell you the order of the digits. A two-cell cage totaling 7 might be 1+6, 2+5, or 3+4 before other restrictions. If one of those cells shares a row with a solved 6, then the 1+6 option may become impossible in that position.

Single-cell cages are direct givens: a one-cell cage with clue 5 is simply a 5. Many online Killer puzzles avoid too many single-cell cages, but they are legal.

The no-repeat rule inside cages

In standard Killer Sudoku, a digit cannot repeat inside a cage. This matters even when repeated digits would make the arithmetic work. A two-cell cage totaling 10 cannot be 5+5 because the cage would repeat 5.

This no-repeat rule is separate from ordinary Sudoku restrictions. If two cage cells are in different rows, different columns, and different boxes, they still cannot repeat if they belong to the same cage.

Some variant puzzles allow cage repeats or say that repeats are allowed when cells do not see each other. Treat that as a special rule. If no special rule is stated, assume cage digits do not repeat.

How to start playing Killer Sudoku

Start with the smallest and most extreme cages. Low totals and high totals have fewer possible combinations, so they give you the first useful restrictions. A 3-cell cage totaling 6 must be 1+2+3; a 3-cell cage totaling 24 must be 7+8+9.

Next, ask where those digits can sit. If a forced cage lies entirely inside one box, all of its digits are locked into that box. If the same cage also touches one row or column in a useful way, ordinary Sudoku eliminations often follow.

Keep notes light at the beginning. Write exact combinations for forced or nearly forced cages, but do not fill every cell with every possible digit. The best early progress usually comes from combining one cage sum with one row, column, or box restriction.

The Rule of 45

Every complete row, column, and 3x3 box in a 9x9 Sudoku totals 45, because 1+2+3+4+5+6+7+8+9 = 45. Killer Sudoku makes that fact useful because cage sums can be added and subtracted.

If the cages fully inside a box add to 41 and one cell in the box is not covered by those cages, that uncovered cell must be 4. If cages mostly inside a box add to 52 but one cage cell sticks outside the box, the outside cell must be 7.

The Rule of 45 is usually the first strategy to learn after the rules. It explains innies and outies, and it turns messy cage layouts into clean sums.

Useful combinations for beginners

You do not need to memorize every Killer Sudoku combination before playing. Start with forced extremes, because they are easy to remember and appear often in beginner puzzles.

A combination tells you the group of digits in a cage, not their positions. A 17 cage in two cells is 8+9, but row, column, and box rules still decide which cell is 8 and which is 9.

Mini worked example

Imagine a 3-cell cage with total 6 in the upper-left box. The only possible digits are 1, 2, and 3. That means no other cell in that same 3x3 box can be 1, 2, or 3 if the cage is fully inside the box.

Now suppose one cell of that cage lies in a row that already contains a 1. That cell cannot be 1, so it must be 2 or 3. If another cage or column clue removes 2, the cell is 3. You started with a cage sum, then used normal Sudoku logic to place a digit.

That is the heart of Killer Sudoku: cage arithmetic creates a small set of candidates, and Sudoku logic turns that set into placements.

Common rule mistakes

The first mistake is allowing repeated digits inside a cage. Unless the puzzle says otherwise, 5+5 is not allowed in a two-cell cage totaling 10.

The second mistake is treating a cage combination as an ordered answer. If a cage is 1+2+3, you know the digits in the cage, but not which digit goes in which cell.

The third mistake is forgetting normal Sudoku rules. Cage sums never replace rows, columns, and boxes; they work alongside them.

The fourth mistake is over-noting. If you write every possible combination everywhere, the useful information gets buried. Note the cage totals that are forced, nearly forced, or tied to a specific row, column, or box.

Rule variations to watch for

Most online and newspaper Killer Sudoku puzzles use the standard no-repeat cage rule. However, variant setters sometimes change that rule. A puzzle may say cage repeats are allowed, cages may not always have unique sums, or extra variant constraints may be added.

Always read the puzzle instructions before solving a variant. On this site, the playable Killer Sudoku follows the standard rule set: rows, columns, boxes, cage sums, and no repeats inside a cage.

What to learn next

Once the rules feel natural, the fastest progress comes from practicing on real grids and learning the three core follow-up topics: combinations, the Rule of 45, and general Killer Sudoku strategy.

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