1. Start with locked combinations
Scan for short runs with extreme sums, the ones that can be made only one way. A two-cell 3 is 1 and 2; a two-cell 17 is 8 and 9; a three-cell 7 is 1, 2 and 4. You may not know the order, but you know the digits, and that is enough to begin. The full set is on the combinations page.
2. Use intersections
This is the engine of Kakuro. Every white cell sits on exactly one across run and one down run. List the candidate digits for each run; the cell must be a digit common to both lists. When a locked across-combination of (1, 2) crosses a locked down-combination of (2, 9), the shared digit 2 fixes the cell. Solve that cell, then re-evaluate both runs.
3. Keep candidate notes
On anything past easy, pencil the possible digits into each cell. As you fix cells, cross the used digit out of the other cells in both of its runs. Most of the puzzle falls out of disciplined elimination rather than clever leaps. The on-screen notes mode does exactly this.
4. Watch the remaining sum
As a run fills, the remaining cells must add up to the remaining sum using only unused digits. A two-cell remainder needing 4 from the digits left can only be certain pairs. Constantly recompute "what sum is left, across how many cells, from which digits" and the options collapse quickly.
5. The 45 rule for blocks
When a region encloses a full column or row segment of nine cells, those cells hold 1 through 9 and sum to 45. Add up the clue sums that feed the region and compare to a multiple of 45; the difference reveals a single cell's value. This is the heavy tool for expert grids and rarely needed below that.
6. Last resort: the two-candidate test
On the toughest puzzles you may reach a cell with exactly two candidates and no immediate deduction. Provisionally take one, follow the consequences a few steps, and if it forces a contradiction the other candidate is correct. Use this sparingly; a well-made Kakuro almost never requires it. Sharpen all of this on a live puzzle.
Frequently asked questions
What is the best Kakuro solving technique?+
Intersection. Find a cell where two runs cross, list the candidate digits for each run, and the cell must be a digit that appears in both lists. When only one digit is shared, the cell is solved. Chaining intersections is how almost every Kakuro is cracked.
What is the 45 rule in Kakuro?+
When a block of runs is bounded so that a full set of nine cells is enclosed, those cells must contain 1 through 9 exactly once, totalling 45. Comparing 45 against the surrounding clue sums lets you deduce a single missing or extra cell. It is the cross-sums cousin of the same idea in Sudoku.
How do I solve hard Kakuro puzzles?+
Lean harder on candidate notes. Pencil every possible digit into each cell, then eliminate relentlessly using locked combinations and intersections. On expert grids you will also use the 45 rule and occasionally a what-if test on a cell with just two candidates.