Killer Sudoku rules: cages, sums and no repeated digits

Killer Sudoku uses the usual Sudoku rules: every row, column and box contains the digits 1–9 once each. Each outlined cage must also add to its small target number, with no repeated digit anywhere inside that cage.

Read the two kinds of boundaries

The thick square boundaries divide the grid into nine boxes, each containing nine cells. The smaller outlined groups are cages. A cage can sit inside a box or cross a box boundary; its total applies to every cell inside its own outline.

A small number printed at a cage's corner is a target sum. It is not a digit already placed in that cell. A two-cell cage marked 3 contains 1 and 2, because they are distinct positive digits whose sum is 3. You still need other clues to decide which cell contains which digit.

Constraint	What must be true
Row	Each digit from 1 through 9 appears once
Column	Each digit from 1 through 9 appears once
Box	Each digit from 1 through 9 appears once
Cage	Its distinct digits add to the printed total

A correct placement satisfies all four constraints simultaneously. A sum that works arithmetically can still be wrong because it repeats a digit in a column.

A combination is not an arrangement

Consider a two-cell cage with total 10. Its possible unordered combinations are 1+9, 2+8, 3+7 and 4+6. The apparent alternative 5+5 is forbidden by the cage rule, even if the two cells occupy different rows and boxes.

Suppose one cell can only contain 1 or 2 after checking its row, column and box. That leaves the combinations 1+9 and 2+8. If the other cell's column already contains 9, remove 1+9. The restricted cell must then be 2 and its partner 8.

The arithmetic alone did not settle the order. The column restriction supplied the missing information. This is the central habit in Killer Sudoku: alternate between sums and ordinary Sudoku restrictions.

Start with short, restrictive cages

1. Fill any single-cell cage with its target digit.
2. Identify small or large totals in short cages.
3. Write the possible digit sets before trying arrangements.
4. Remove sets that cannot fit the surrounding rows, columns or boxes.
5. Return to affected cells after every placement.

A three-cell cage totaling 6 must contain 1, 2 and 3. A three-cell cage totaling 24 must contain 7, 8 and 9. These are useful starting points, but neither tells you the order without additional restrictions.

For a less restrictive three-cell cage totaling 7, the only set is 1+2+4. If its cells all share a row, those three digits cannot occur elsewhere in that row. A cage crossing several rows does not reserve all its digits in every row it touches.

Use notes as possibilities

A pencil note means a digit is still possible in a particular cell. It does not mean that digit belongs to every surviving cage combination. When a combination disappears, revisit the notes that depended on it.

Avoid writing a whole cage's digit union into every cell without checking its peers. For example, a cage may need a 7 somewhere while one of its cells sees a placed 7 in the same column. That cell cannot contain 7, although the cage still must.

If a cell loses every candidate, stop and inspect the last deduction. Do not repair the position by inserting a digit that breaks a sum. A contradiction often comes from confusing a possible arrangement with a forced one.

Check understanding before increasing difficulty

Try explaining why 5+5 cannot fill a two-cell total of 10. Then explain why a total of 3 establishes the digits but not their order. Finally, find a cell restriction that would settle that order. These questions test separate parts of the rules.

You do not need advanced techniques to begin. Accurate cage reading, complete combinations and routine row-column-box checks give you a reliable first solving loop. Once this feels comfortable, learn how each full row or box totals forty-five.

Where to play

Kudoku includes interactive Killer Sudoku practice, manual notes and five difficulty tracks with 25,000 campaign puzzles. It is free to download; the campaign is playable in order, and optional Premium adds convenience tools such as Auto Notes. Start with an easier track and explain each placement before entering it.