Kakuro: rules, combinations and free puzzles online
Kakuro is a crossword made of numbers. Every run of white cells has a clue giving its total, and you fill the runs with distinct digits from 1 to 9. Play kakuro online free here at four ranks.
The name is a shortening of the Japanese for “addition cross”, and the puzzle is also known as Cross Sums. The secret weapon is a short list of kakuro combinations that can only be made one way.
Opens in your browser. No sign-up, no ads.
The rules
- Fill every white cell with a digit from 1 to 9.
- Each clue cell is split by a diagonal. The number above the diagonal is the total of the run to its right (across); the number below is the total of the run beneath it (down).
- Each run of white cells must add up to its clue.
- No digit repeats within a run. The same digit may appear twice in a row or column if it is in two different runs.
How to start
Learn the kakuro combinations
Most totals can be made in several ways, but some can only be made one way. These are the ones to look for first: 3 in two cells is always 1 + 2, 17 in two is always 8 + 9, and 24 in three is always 7 + 8 + 9.
| Run length | Unique totals and their digits |
|---|---|
| 2 cells | 3 = 1 + 2 4 = 1 + 3 16 = 7 + 9 17 = 8 + 9 |
| 3 cells | 6 = 1 + 2 + 3 7 = 1 + 2 + 4 23 = 6 + 8 + 9 24 = 7 + 8 + 9 |
| 4 cells | 10 = 1 + 2 + 3 + 4 11 = 1 + 2 + 3 + 5 29 = 5 + 7 + 8 + 9 30 = 6 + 7 + 8 + 9 |
| 5 cells | 15 = 1 + 2 + 3 + 4 + 5 16 = 1 + 2 + 3 + 4 + 6 34 = 4 + 6 + 7 + 8 + 9 35 = 5 + 6 + 7 + 8 + 9 |
| 6 cells | 21 = 1 + 2 + 3 + 4 + 5 + 6 22 = 1 + 2 + 3 + 4 + 5 + 7 38 = 3 + 5 + 6 + 7 + 8 + 9 39 = 4 + 5 + 6 + 7 + 8 + 9 |
| 7 cells | 28 = 1 + 2 + 3 + 4 + 5 + 6 + 7 29 = 1 + 2 + 3 + 4 + 5 + 6 + 8 41 = 2 + 4 + 5 + 6 + 7 + 8 + 9 42 = 3 + 4 + 5 + 6 + 7 + 8 + 9 |
| 8 cells | 36 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 37 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 9 38 = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 39 = 1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 40 = 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 41 = 1 + 2 + 3 + 5 + 6 + 7 + 8 + 9 42 = 1 + 2 + 4 + 5 + 6 + 7 + 8 + 9 43 = 1 + 3 + 4 + 5 + 6 + 7 + 8 + 9 44 = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 |
| 9 cells | 45 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 |
Every entry in this chart was generated by computer, checking all sets of distinct digits, so you can trust it.
Cross the runs
Where an across run and a down run meet, the shared cell must use a digit allowed by both.
Use the missing digit
A run of nine cells always totals 45. A run of eight cells misses exactly one digit, and that digit is 45 minus the clue. Long runs are easier than they look.
Common mistakes
- Repeating a digit within a run.
- Reading the clue halves the wrong way round: across is top-right, down is bottom-left.
- Treating a whole row as one run when a black cell splits it in two.
How the ranks scale difficulty
The same four ranks apply here as everywhere on the site. Lemma is a gentle warm-up, Proposition needs a real idea or two, Theorem is near-minimal with almost every clue load-bearing, and Conjecture is the sparsest of all, so expect to think hard.
Higher ranks lean less on the unique combinations and more on crossing several flexible runs at once.
There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it. Every type also has a 30-puzzle collection that climbs from Lemma to Conjecture. Every puzzle is checked to have exactly one solution that you can reach by logic alone, with no guessing.
Frequently asked questions
What are kakuro combinations?
The sets of distinct digits that can make a given total in a given number of cells. Some totals, like 16 in two cells (7 + 9), can be made only one way.
Can digits repeat in kakuro?
Not within a run. The same digit can appear elsewhere in the same row or column if it belongs to a different run.
Which number is the across clue?
The one above the diagonal, at the top right of the clue cell. The down clue is below the diagonal, at the bottom left.
Do you need to be good at maths for kakuro?
Only at small sums. The real skill is logic: crossing runs and eliminating combinations.
Professor Hoot’s hints teach the next logical step whenever you’re stuck.