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Kakuro Solver
Two kinds of solver tools in one place: a combination calculator that lists every valid digit set for any sum and run length, and an in-game hint engine that highlights the next forced cell and explains the logic. Use whichever fits your current block.
Both run entirely in your browser — no account, no install, no cost.
Combination calculator
The Kakuro helper calculator solves the first problem every solver hits: "what digits are even possible in this run?" Enter a sum target and a run length, and it returns every valid set of distinct digits (1–9) that produce that total.
2 cells · sum 3
{1, 2}
Only one combination — both digits are forced.
3 cells · sum 7
{1, 2, 4}
Only one combination — all three digits are forced.
4 cells · sum 15
6 combinations
Intersecting runs narrow it further.
The full combination reference lists every sum-and-length pair in one table — useful when you need to scan across multiple runs at once.
In-game solver tools
The live game at freekakuro.com includes three features that help you work through stuck positions:
Hint
Highlights the most constrained unsolved cell and explains why a particular digit is forced there. Useful for a single nudge without spoiling the whole board.
Candidates
Toggles a 3×3 digit matrix inside each white cell, showing which values are still possible. Manually cross out digits as you eliminate them from runs.
Auto play
Advances through all currently forced moves in one step. When it stops, you are at a genuine choice point that requires deeper technique — no more trivially forced cells remain.
How to solve Kakuro step by step
Every Kakuro puzzle has a logical solution — no guessing is required. The process is systematic:
- Find unique combinations. Scan every run for a sum/length pair that maps to only one digit set. A 2-cell sum of 3 is always 2; a 3-cell sum of 6 is always 3. Mark those digits as candidates in the relevant cells. Use the combination reference to speed this up.
- Apply cross-sum intersection. For each cell, intersect the candidates from its across run with the candidates from its down run. Any digit not in both sets is impossible — eliminate it.
- Look for singles. After intersection, some cells may have only one remaining candidate. Fill those cells and remove the placed digit from the candidate sets of every other cell in the same runs.
- Use residual sums. Once some cells in a run are filled, subtract their totals from the clue. Treat the remaining empty cells as a new, shorter run and repeat the combination lookup.
- Apply advanced techniques if stuck. Locked sets, min/max bounds, and combination pruning cover most hard positions. The technique library explains each one with examples.
Solving techniques
Unique combinations
Some sum/length pairs have only one valid digit set. Identifying these gives you free cell values with no further work. Every forced combination is listed in the reference chart.
Cross-sum intersection
Where an across run and a down run share a cell, the digit must appear in both sets of candidates. Intersection often eliminates all but one option.
Residual sums
Once some cells in a run are filled, subtract their values from the clue to find the remaining sum. Apply combination logic to the shorter remaining run.
Min / max bounds
Every run has a minimum possible sum (1+2+…+n) and a maximum (9+8+…+(10-n)). Cells that cannot satisfy both constraints are eliminated immediately.
Locked sets
If k cells in a run can only contain k candidates, those candidates are locked there and can be removed from other cells in the same run.
Combination pruning
Iteratively discard any candidate combination that contradicts a filled cell or an intersecting run's remaining options. What survives constrains the remaining cells.
Which solver tool should I use?
Stuck on a specific clue: Use the combination calculator — enter the sum and run length to see every valid digit set.
Need a single nudge in the live game: Hit the hint button — it highlights one cell and explains the forcing logic.
Want to skip forced moves: Use auto play — it advances through all trivially forced cells so you can focus on the hard positions.
Want to understand the logic: Read the technique library — each technique has a worked example.
New to Kakuro: Start with the rules page, then try easy puzzles where forced moves appear quickly and the solving loop is easy to follow.
Kakuro solver FAQ
- How do I solve a Kakuro puzzle?
- Find runs where the sum forces a unique combination. Cross-reference across and down runs that share cells. Eliminate impossible candidates, fill forced cells, and repeat. The technique library covers what to do when basic elimination runs out.
- What does the combination calculator do?
- It lists every valid set of distinct digits (1–9) that sum to a target with a given number of cells. This is the starting point for most Kakuro deductions. The helper calculator provides instant lookup for any sum and run length.
- Can I solve Kakuro without guessing?
- Yes. Every puzzle on Free Kakuro is verified to have a unique solution reachable by pure logic. If you feel stuck, you likely have not exhausted the current constraint set — a hint or auto play step will show the next forced move.
- What is the hardest part of solving Kakuro?
- Managing candidates across multiple intersecting runs simultaneously. Easy puzzles have short, well-constrained runs where forced moves are obvious. Hard and ultra-hard puzzles require tracking 5–7 cell runs across both axes where the intersection logic is several steps deep.
- Is there a free Kakuro solver I can use online?
- Free Kakuro provides a combination calculator, a hint engine, and auto play — all free, no account required. These cover the two main solver needs: knowing which digits are possible in a run, and finding the next forced move in a live puzzle.