Killer Sudoku cage combinations: complete 2–4 cell tables
Look up every distinct-digit combination for two-, three- and four-cell cages. Learn how to filter the tables with cell restrictions and solved digits.
Updated 2026-11-13
A Killer Sudoku cage combination is a set of distinct digits from 1–9 that adds to the cage total. The tables below list every combination for two-, three- and four-cell cages; digit order is ignored, so 1+2 and 2+1 are the same entry.
How to read the tables
Count the cells in the entire cage before looking up its sum. A three-cell cage with one filled digit is still a three-cell cage, although you can subtract that digit and reason about its two remaining cells separately. Use the right table for the quantity you are actually analysing.
Each entry gives a possible set, not a placement. For a two-cell total of 3, the set is 1+2, but either digit could go in either cell until other constraints decide. If a total does not appear in a size's table, no distinct-digit combination exists for that size.
The list includes thirty-six pairs, eighty-four triples and one hundred twenty-six quadruples. These count unordered sets. They do not count the different ways a set can be arranged in cells, and they do not claim that every listed set fits your particular board.
Two-cell cages
| Sum | All unordered combinations |
|---|---|
| 3 | 1+2 |
| 4 | 1+3 |
| 5 | 1+4; 2+3 |
| 6 | 1+5; 2+4 |
| 7 | 1+6; 2+5; 3+4 |
| 8 | 1+7; 2+6; 3+5 |
| 9 | 1+8; 2+7; 3+6; 4+5 |
| 10 | 1+9; 2+8; 3+7; 4+6 |
| 11 | 2+9; 3+8; 4+7; 5+6 |
| 12 | 3+9; 4+8; 5+7 |
| 13 | 4+9; 5+8; 6+7 |
| 14 | 5+9; 6+8 |
| 15 | 6+9; 7+8 |
| 16 | 7+9 |
| 17 | 8+9 |
Three-cell cages
| Sum | All unordered combinations |
|---|---|
| 6 | 1+2+3 |
| 7 | 1+2+4 |
| 8 | 1+2+5; 1+3+4 |
| 9 | 1+2+6; 1+3+5; 2+3+4 |
| 10 | 1+2+7; 1+3+6; 1+4+5; 2+3+5 |
| 11 | 1+2+8; 1+3+7; 1+4+6; 2+3+6; 2+4+5 |
| 12 | 1+2+9; 1+3+8; 1+4+7; 1+5+6; 2+3+7; 2+4+6; 3+4+5 |
| 13 | 1+3+9; 1+4+8; 1+5+7; 2+3+8; 2+4+7; 2+5+6; 3+4+6 |
| 14 | 1+4+9; 1+5+8; 1+6+7; 2+3+9; 2+4+8; 2+5+7; 3+4+7; 3+5+6 |
| 15 | 1+5+9; 1+6+8; 2+4+9; 2+5+8; 2+6+7; 3+4+8; 3+5+7; 4+5+6 |
| 16 | 1+6+9; 1+7+8; 2+5+9; 2+6+8; 3+4+9; 3+5+8; 3+6+7; 4+5+7 |
| 17 | 1+7+9; 2+6+9; 2+7+8; 3+5+9; 3+6+8; 4+5+8; 4+6+7 |
| 18 | 1+8+9; 2+7+9; 3+6+9; 3+7+8; 4+5+9; 4+6+8; 5+6+7 |
| 19 | 2+8+9; 3+7+9; 4+6+9; 4+7+8; 5+6+8 |
| 20 | 3+8+9; 4+7+9; 5+6+9; 5+7+8 |
| 21 | 4+8+9; 5+7+9; 6+7+8 |
| 22 | 5+8+9; 6+7+9 |
| 23 | 6+8+9 |
| 24 | 7+8+9 |
Four-cell cages
| Sum | All unordered combinations |
|---|---|
| 10 | 1+2+3+4 |
| 11 | 1+2+3+5 |
| 12 | 1+2+3+6; 1+2+4+5 |
| 13 | 1+2+3+7; 1+2+4+6; 1+3+4+5 |
| 14 | 1+2+3+8; 1+2+4+7; 1+2+5+6; 1+3+4+6; 2+3+4+5 |
| 15 | 1+2+3+9; 1+2+4+8; 1+2+5+7; 1+3+4+7; 1+3+5+6; 2+3+4+6 |
| 16 | 1+2+4+9; 1+2+5+8; 1+2+6+7; 1+3+4+8; 1+3+5+7; 1+4+5+6; 2+3+4+7; 2+3+5+6 |
| 17 | 1+2+5+9; 1+2+6+8; 1+3+4+9; 1+3+5+8; 1+3+6+7; 1+4+5+7; 2+3+4+8; 2+3+5+7; 2+4+5+6 |
| 18 | 1+2+6+9; 1+2+7+8; 1+3+5+9; 1+3+6+8; 1+4+5+8; 1+4+6+7; 2+3+4+9; 2+3+5+8; 2+3+6+7; 2+4+5+7; 3+4+5+6 |
| 19 | 1+2+7+9; 1+3+6+9; 1+3+7+8; 1+4+5+9; 1+4+6+8; 1+5+6+7; 2+3+5+9; 2+3+6+8; 2+4+5+8; 2+4+6+7; 3+4+5+7 |
| 20 | 1+2+8+9; 1+3+7+9; 1+4+6+9; 1+4+7+8; 1+5+6+8; 2+3+6+9; 2+3+7+8; 2+4+5+9; 2+4+6+8; 2+5+6+7; 3+4+5+8; 3+4+6+7 |
| 21 | 1+3+8+9; 1+4+7+9; 1+5+6+9; 1+5+7+8; 2+3+7+9; 2+4+6+9; 2+4+7+8; 2+5+6+8; 3+4+5+9; 3+4+6+8; 3+5+6+7 |
| 22 | 1+4+8+9; 1+5+7+9; 1+6+7+8; 2+3+8+9; 2+4+7+9; 2+5+6+9; 2+5+7+8; 3+4+6+9; 3+4+7+8; 3+5+6+8; 4+5+6+7 |
| 23 | 1+5+8+9; 1+6+7+9; 2+4+8+9; 2+5+7+9; 2+6+7+8; 3+4+7+9; 3+5+6+9; 3+5+7+8; 4+5+6+8 |
| 24 | 1+6+8+9; 2+5+8+9; 2+6+7+9; 3+4+8+9; 3+5+7+9; 3+6+7+8; 4+5+6+9; 4+5+7+8 |
| 25 | 1+7+8+9; 2+6+8+9; 3+5+8+9; 3+6+7+9; 4+5+7+9; 4+6+7+8 |
| 26 | 2+7+8+9; 3+6+8+9; 4+5+8+9; 4+6+7+9; 5+6+7+8 |
| 27 | 3+7+8+9; 4+6+8+9; 5+6+7+9 |
| 28 | 4+7+8+9; 5+6+8+9 |
| 29 | 5+7+8+9 |
| 30 | 6+7+8+9 |
Filter a row of combinations
Take a two-cell cage totaling 10. The table lists 1+9, 2+8, 3+7 and 4+6. Suppose cell A has only 1 or 2 available, and cell B has only 8 or 9 available. Only the first two combinations can fit those cells. If B's column already contains 9, eliminate 1+9 and fill A with 2 and B with 8.
This illustrates two separate checks. First, each required digit must have somewhere to go. Second, all digits in a combination must fit simultaneously. If two different digits can each go only in the same single cell, the combination fails even though both digits appear somewhere in the notes.
For a three-cell cage totaling 10 with a solved 2, subtract 2 to get a remaining sum of 8. The pair table offers 1+7, 2+6 and 3+5, but 2+6 is forbidden: the full cage already contains 2. The remaining cells must use 1+7 or 3+5 before you apply their row, column and box restrictions.
Use extreme totals as anchors
The smallest three-cell total is 6, made by 1+2+3. The largest is 24, made by 7+8+9. For four cells the extremes are 10 and 30. Each extreme has one combination, which makes it a useful starting point.
A single combination still leaves an ordering problem. If a four-cell total of 10 occupies a single row, its digits 1, 2, 3 and 4 are reserved within those cells in that row. If the cage crosses rows, that same row exclusion does not automatically apply to all four digits.
Keep combination notes and cell notes consistent
After placing a digit, remove combinations that omit it or require it twice. Then revisit each cell and delete digits supported by no surviving arrangement. When a row or column loses a candidate, check whether that change removes another cage combination.
Do not confuse a digit present in some combinations with a digit required in all combinations. For example, seeing 9 in one listed pair does not establish that the cage contains 9. Only a digit common to every surviving set is compulsory, and its position may still be unresolved.
To practise, cover the combinations beside one total and rebuild them with increasing digits. Starting each set with its smallest digit prevents duplicates. Then compare with the table and explain one way the surrounding board could rule out a set. That connects arithmetic recall to actual solving.
Where to play
Kudoku combines cage sums with ordinary Sudoku constraints and offers cage-aware pencil notes. Its five difficulty tracks contain 25,000 campaign puzzles. Keep this table nearby while learning, then try recalling the restrictive totals before checking the list.