Kakuro combinations chart

Kakuro (also called cross sums) gives you a grid of white cells grouped into entries, each with a target sum. The digits 1 through 9 must fill every white cell, with no digit repeating inside the same entry. Combinations are the foundation of the whole solving process: figuring out which sets of digits can produce a given sum in a given number of cells.

Take a 2-cell entry with sum 3. The only pair of distinct digits from 1-9 that adds to 3 is {1, 2}. That entry is forced. You still need cross-entry logic to figure out which cell gets the 1 and which gets the 2, but knowing the digits narrows things immediately. Compare that with a 3-cell entry with sum 15, which has seven valid combinations. The more combinations an entry allows, the more you need intersecting constraints to pin things down.

The practical approach: scan your grid for entries with few combinations first. Two-cell entries at the extremes (sums 3, 4, 16, 17) and three-cell entries at the extremes (sums 6, 7, 23, 24) are always forced. Start there, place what you can, and let the ripple effects reduce candidates elsewhere.

When multiple combinations survive for an entry, check which digits appear in every combination. If the digit 5 shows up in all of them, 5 must be somewhere in that entry. Combine that with constraints from the crossing entry, and you can often identify the exact cell.

For harder puzzles, you will need to track candidates cell by cell. Write the possible digits in each cell (use notes mode in the game), then eliminate based on entry combinations and cross-referencing. When a cell has one candidate left, fill it. This triggers more eliminations, and the puzzle unravels from there.

This chart covers all 120 valid entry/sum pairs. The data is the same set used by our kakuro solver and hint engine, so what you see here matches what the game uses internally.