Rules · Strategy · Examples
How to Play Kakuro
Kakuro is a crossword-style number puzzle. Your goal is to fill white cells with digits 1–9 so that each connected run of white cells sums to the clue shown in the adjacent black cell, with no digit repeated within any run. No guessing required — every puzzle solves by logic alone.
This guide walks you through the grid layout, clue notation, the two core rules, and the step-by-step techniques beginners use to crack their first puzzle.
The two rules of Kakuro
Rule 1 — Sum
Every run of white cells must add up exactly to the number shown in the adjacent clue cell. Across runs use the upper-right clue; down runs use the lower-left clue.
Rule 2 — No repeats
Within a single run, each digit 1–9 may appear at most once. The same digit can appear in the same row or column if it belongs to a different run.
How to play Kakuro: step by step
- 1
Understand the grid layout
A Kakuro board looks like a crossword. Black cells divide the grid; white cells are the ones you fill. Some black cells contain clue numbers — these are clue cells. Completely black cells with no number are just walls.
- 2
Read the clue cells
Each clue cell is split by a diagonal line. The number in the upper-right triangle is the target sum for the white cells stretching to the right (the across run). The number in the lower-left triangle is the target sum for the white cells stretching downward (the down run). Not every clue cell has both — it depends on whether white cells exist in that direction.
- 3
Know the two constraints
Every white cell must obey two rules simultaneously: (1) the digits in each run must add up exactly to the clue, and (2) no digit may repeat within a single run. Digits 1–9 are the only valid entries. Zero is not allowed.
- 4
Find unique-combination runs
Some runs have exactly one valid digit set for their sum and length. A 2-cell run summing to 3 can only be {1, 2}. A 3-cell run summing to 6 can only be {1, 2, 3}. These are your entry points — identify them first using the combination reference.
- 5
Use intersection logic
Every white cell sits in both an across run and a down run. The digit you place must satisfy both. If the across run constrains the cell to {1, 4} and the down run constrains it to {4, 7}, the only value that satisfies both is 4. This kind of intersection reasoning is the core of Kakuro solving.
- 6
Track candidates and residual sums
As you fill in digits, the sum remaining for unresolved cells in a run decreases. If a 4-cell run sums to 20 and you have placed a 3 and a 7, the two remaining cells must sum to 10 — and you know the digit set from the combination table. Use candidate mode to track which digits are still possible in each cell.
- 7
Finish with pure deduction
Continue applying these techniques until every white cell has a forced value. A valid puzzle never requires guessing. If you are stuck, revisit candidate lists and check every intersection.
Essential techniques for new players
Combination lookup
For any run sum and length there is a finite list of valid digit sets. Short or extreme sums often have only one valid set, making those cells easy to fill. The combination reference lists every valid set for every sum and length.
Candidate tracking
Write down (or use the game's candidate overlay) which digits are still possible in each cell. As you eliminate options, cells with only one remaining candidate can be filled immediately.
Intersection elimination
A cell at the crossing of an across run and a down run must satisfy both constraints. If the across constraint allows 8 and the down constraint allows 6, the cell must be 5.
Residual sums
Once some cells in a run are filled, subtract those values from the run total to find the sum that the remaining cells must hit. The smaller residual often has far fewer valid combinations than the original run.
Ready to go deeper? The technique library covers intersection logic, naked pairs, X-wing patterns, and more.
Practice by difficulty
The best way to learn how to play Kakuro is to play it. Start with easy and work up.
Easy Kakuro
Short runs, many forced combinations, low constraint density. Perfect for learning the rules and practising combination lookup. Easy Kakuro guide →
Medium Kakuro
Longer runs and denser intersections. Candidate tracking becomes important. Good for building fluency once easy is comfortable. Medium Kakuro guide →
Hard Kakuro
Sparse forced moves, dense intersections. You will rely heavily on residual sums and intersection elimination to make progress. Hard Kakuro guide →
How to play Kakuro — FAQ
- What is Kakuro and how do you play it?
- Kakuro is a number-logic puzzle. Fill white cells with digits 1–9 so each run sums to its clue and no digit repeats within a run. Every valid puzzle has one unique solution reachable by deduction.
- How do you read the clues?
- Black clue cells are split diagonally. Upper-right number = across sum (cells going right). Lower-left number = down sum (cells going down). If only one direction has white cells, only that triangle shows a number.
- Can digits repeat in Kakuro?
- No digit may repeat within a single run. The same digit can appear in the same row or column if it belongs to a different run — that is perfectly legal.
- Where do you start in a Kakuro puzzle?
- Look for runs with only one valid digit combination — often short runs with extreme sums (very low or very high). These give you immediate placements. Use the combination reference to find them fast.
- Do you ever need to guess?
- No. A correctly constructed Kakuro puzzle always has exactly one solution reachable by logic. If you feel stuck, try candidate tracking and intersection elimination before concluding that guessing is necessary.
- Is Kakuro the same as Cross Sums?
- Yes. "Cross Sums" is the original English name for the puzzle; "Kakuro" is the name popularised in Japan and now the most common name worldwide. The rules are identical. See the Kakuro Cross Sums page for more.