Killer Sudoku Combinations

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Published May 8, 2026 · 18 min read

Killer Sudoku combinations are the arithmetic engine of every Killer puzzle. The cage total tells you the sum, the cage size tells you how many digits are involved, and the no-repeat rule usually means those digits must all be different.

This guide gives you the combination charts you actually need while solving: every 2-cell, 3-cell, and 4-cell cage sum, the minimum and maximum totals for larger cages, and a practical workflow for turning a long list of combinations into real Sudoku eliminations.

What Killer Sudoku combinations are

A Killer Sudoku cage is a group of cells with a small total in the corner. If a cage has two cells and the clue is 10, the digits might be 1+9, 2+8, 3+7, or 4+6. Those are the cage combinations.

Most Killer Sudoku puzzles add one more rule: digits cannot repeat inside a cage. That is why 5+5 is not allowed in a 2-cell 10 cage unless the puzzle explicitly says repeats are permitted.

How to use a combination chart

Do not copy every combination into the grid. Use the chart to find the possible groups, then immediately filter them through Sudoku rules. If a row already contains 8, every combination placing 8 in a cell in that row becomes weaker or impossible.

The best combinations are either forced, nearly forced, or restricted to a useful house. A cage with four possible digit groups is still valuable if all four groups contain a 7, or if all possible positions for 7 sit in the same box.

2-cell Killer Sudoku combinations

Two-cell cages are the easiest to memorize and the most common source of early progress. The extreme sums are forced, and the middle sums quickly become pairs once nearby digits are eliminated.

3-cell Killer Sudoku combinations

Three-cell cages give more options, but the low and high ends are still very tight. Learn 6, 7, 23, and 24 first, then use the full chart when a cage sits in a crowded row, column, or box.

4-cell Killer Sudoku combinations

Four-cell cages look broad, but their extremes are powerful. A 4-cell 10 cage is exactly 1+2+3+4, while a 4-cell 30 cage is exactly 6+7+8+9.

Middle totals have many choices, so focus on overlap: which digits appear in every option, which digits never appear, and whether a pair of cells can only contain the same two digits.

Minimum and maximum cage sums

Before listing combinations, check whether a cage total is even possible. The lowest sum for k cells uses 1 through k; the highest uses the largest k digits.

This table is also useful for spotting forced extremes. If a cage is one away from the minimum or maximum, it often has only one or two realistic groups after normal Sudoku restrictions.

How to handle 5+ cell cages

Large cages are usually easier through complements than through long lists. All digits 1 to 9 add to 45, so a 5-cell cage totaling 35 is the same as saying the four missing digits total 10. The missing digits must be 1+2+3+4, so the cage contains 5+6+7+8+9.

Use the same idea for 6-cell, 7-cell, and 8-cell cages. A 7-cell cage is often best understood by the two digits it does not contain.

How to reduce combinations

A raw combination is only the start. Remove any digit already placed in the same row, column, or box as a cage cell. Then ask whether the remaining digits can actually be arranged across the cage cells.

Suppose a 3-cell cage totals 15. The chart lists 1+5+9, 1+6+8, 2+4+9, 2+5+8, 2+6+7, 3+4+8, 3+5+7, and 4+5+6. If one cage cell sees every 9 in its row and box, every option that requires 9 in that cell disappears. If 9 can go nowhere in the cage, all 9-combinations disappear.

Combinations and the rule of 45

Each row, column, and 3x3 box totals 45. That lets you create new cage sums from groups of cages. If cages inside a box total 42 and one uncovered cell remains, that cell is 3.

The rule of 45 is especially strong when it creates a two-cell sum. A pair totaling 16 can only be 7+9, and a pair totaling 4 can only be 1+3. Once the arithmetic gives you a small cage, the combination chart turns it into Sudoku logic.

Notation that stays readable

Keep cage combinations separate from cell candidates. Cell candidates answer "what can go here?" Cage combinations answer "which group can fill this cage?" Mixing the two makes hard Killer puzzles feel messier than they are.

Write full cage combinations only when there are a few left. For broad totals, note forced digits, excluded digits, or a short label such as "no 9" or "must include 4". After a placement, update the touched cage immediately.

Worked examples

Example 1: a 2-cell 17 cage is 8+9. If one of its cells is in a column that already has 9, that cell must be 8 and the other cell must be 9.

Example 2: a 3-cell 7 cage is 1+2+4. If the cage occupies two cells in one box and one cell in another box, those three digits are locked to the cage. None of 1, 2, or 4 can repeat inside the cage, and any solved 1, 2, or 4 nearby can place the rest.

Example 3: a box has cages totaling 50 with one outie outside the box. Since the box itself totals 45, the outie is 5. That single digit may reduce its cage to a forced pair.

Common Killer Sudoku combination mistakes

The first mistake is allowing repeated digits in a cage by accident. In the standard rules, 5+5 is not a valid 10 pair.

The second mistake is treating a combination as a placement. A 3-cell 24 cage tells you the cage uses 7, 8, and 9; it does not tell you which cell receives which digit until row, column, and box logic decide.

The third mistake is over-noting. If a cage has ten possible groups, writing all ten may hide the useful fact that only one digit is forced or only one digit is impossible.

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