Killer Sudoku Cage Sums — Complete Combination Reference

In Killer Sudoku, certain cage sizes and sums have only one possible combination of digits. These "forced" cages are your fastest route to placing digits — no deduction needed, just recognition.

Forced 2-cell cages

2-cell cages with extreme sums have only one valid combination:

Sums 5 through 15 have multiple combinations (e.g. sum 5 could be {1,4} or {2,3}) and require additional constraints to resolve.

Forced 3-cell cages

A 3-cell cage summing to 6 is completely determined — you know all three digits, just not their order within the cage.

The 45 rule in practice

Since every row, column, and box sums to 45, you can calculate "what is left over" when cages overlap with rows or boxes.

Why range matters for large cages

For a 4-cell cage, the minimum possible sum is 1+2+3+4=10 and the maximum is 6+7+8+9=30. Any cage outside this range is impossible. On valid puzzles, this helps you spot whether a cage can possibly contain a particular digit.

Memorization priority

You do not need to memorize every combination. Prioritize: 2-cell extremes (3,4,16,17), 3-cell extremes (6,7,23,24), and the fact that the minimum for any n-cell cage is 1+2+...+n. Everything else follows from these anchors.