How to Play Kakuro
Fill every white square of a kakuro grid with a digit from 1 to 9. Each unbroken line of white squares — a run — must add up to the clue printed in the shaded cell before it, and may not use the same digit twice. Every square belongs to one across run and one down run, so its digit has to satisfy two clues at once. A correct kakuro has exactly one solution and needs no guessing.
The rules, step by step
- 1Fill the white squares with 1 to 9Every white square takes exactly one digit between 1 and 9. There is no zero and no blank square in a finished grid.
- 2Add each run to its clueA run is an unbroken line of white squares. The digits in it must total the number in the shaded cell that starts it — above the diagonal for across, below it for down.
- 3Never repeat a digit inside a runThe digits in one run must all be different. A repeat is allowed elsewhere in the same row or column, as long as it falls in a different run.
- 4Treat a clue as a set of digitsSeventeen in two squares can only be 8 and 9; six in three squares can only be 1, 2 and 3. Looking the set up beats adding numbers together every time.
- 5Use the crossingsEvery white square sits on one across run and one down run at once, so a digit has to satisfy both clues. That overlap is where almost every deduction in the game comes from.
- 6Finish when every square is full and legalThe puzzle is solved the moment all the white squares hold digits, every run hits its total, and no run repeats. There is nothing else to check.
Try it — the rules above, running
New puzzle generates a fresh grid at the size you last chose, Hint fills one square and says which clue settled it, and the three-dot menu holds the combination reference, pencil marks, fill-in-all-marks, check-as-you-go, today’s shared puzzle and the grid size.
Your statistics · 6 × 6
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- Best streak
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This grid
A 6 × 6 interior. The shortest grid here — four runs in five are two or three squares long — and the one to learn the combination table on.
Clues with only one answer
Thirty-four of the 120 possible clues have exactly one set of digits. These twelve are the ones worth knowing by heart.
- 3 in 2 = 1 + 2
- 4 in 2 = 1 + 3
- 16 in 2 = 7 + 9
- 17 in 2 = 8 + 9
- 6 in 3 = 1 + 2 + 3
- 7 in 3 = 1 + 2 + 4
- 23 in 3 = 6 + 8 + 9
- 24 in 3 = 7 + 8 + 9
- 10 in 4 = 1 + 2 + 3 + 4
- 11 in 4 = 1 + 2 + 3 + 5
- 29 in 4 = 5 + 7 + 8 + 9
- 30 in 4 = 6 + 7 + 8 + 9
Keyboard
- Arrows
- Move to the next square
- 1 – 9
- Enter a digit
- Backspace
- Clear the square
- P
- Pencil marks on or off
- C
- Combination reference
- F
- Full screen
How do you read the grid?
- 1Find the shaded cellsEach shaded cell is split by a diagonal line. A number above the diagonal is the total for the run of white squares running to the right; a number below it is the total for the run running down.
- 2Mark where each run endsA run stops at the next shaded cell or at the edge of the grid. A run is never one square long, so if you have found a single white square between two shaded cells, you have misread the layout.
- 3Write the length next to the clueA total means nothing without a length. "16" is forced in two squares and nearly free in five. On paper, solvers write clues as "16/2".
- 4Look up the sets, do not addTurn each clue into the digit sets that can make it. The board does this for you: select a square and press C to see every set both of its clues still allow.
Where should you make the first move?
At a crossing of two tightly constrained clues. The classic opening is a short run with an extreme total — 3, 4, 16 or 17 in two squares — crossing another one. If a 17-in-two ({8, 9}) crosses a 16-in-two ({7, 9}), the shared square must be the 9, because it is the only digit both sets contain. That single square then forces the 8 and the 7 either side of it, and the grid is open.
The other reliable opening is the longest run on the board. Nine squares can only be 1 to 9 totalling 45; eight squares can only be 1 to 9 with one digit missing, and which digit is missing is decided entirely by the total.
What techniques come after the forced clues?
- Cross-elimination — list what a square's across clue allows, list what its down clue allows, and keep only the digits in both. If one survives, write it in.
- Required digits — if every remaining set for a run contains a 9, that run must use a 9 somewhere. If only one of its squares can still take a 9, that square is settled.
- The leftover — when a run has one empty square left, the total names the digit outright. Check it against the no-repeat rule before writing it in.
- Partial sums as a check — a run of four totalling 12 with a 7 already written in needs 5 from its three remaining squares. Three different digits cannot total less than 6, so the 7 is wrong and everything downstream of it is too.
That last one is worth dwelling on, because it is the commonest way to catch a mistake. The smallest total three different digits can make is 1 + 2 + 3 = 6, and the largest is 7 + 8 + 9 = 24. Any run whose remaining squares are asked for less than the minimum or more than the maximum has an error behind it.
How do you avoid the usual beginner mistakes?
- Do not add up the whole row. The no-repeat rule is per run, not per row. Two 4s in the same row are perfectly legal if a shaded cell sits between them.
- Do not leave pencil marks half done. A run with marks in three of its five squares looks more constrained than it is, and every deduction drawn from it is suspect.
- Do not ignore the long runs. They look like the hardest clues and they are the easiest.
- Do not guess to break a deadlock. A correct kakuro never needs it, and a wrong digit propagates so far that undoing it costs more than finding the deduction would have.
How do you win more often?
- Open on a forced clue, not on the shortest runThirty-four of the 120 possible clues allow exactly one set of digits, and about one clue in five on a generated grid is one of them. Find one and you have the contents of a whole run before you have worked out a single square.
- Cross two forced clues and you have a squareIf a 17-in-two crosses a 6-in-three, the first is {8,9} and the second is {1,2,3}. The sets share nothing, so that crossing square is impossible — which means you have misread a clue, and catching that early saves ten minutes.
- Work the long runs first, not lastA nine-square run is always 1 to 9 and an eight-square run is 1 to 9 minus one digit, so the longest runs on a grid are the ones that give up their contents instantly. Beginners avoid them because the totals look large.
- Ask which digits a run cannot do withoutEvery way of totalling 16 in two squares uses a 9. If only one of those two squares can take a 9 — because its down clue rules the 9 out of the other — that square is settled without narrowing anything else down first.
- Pencil a whole run at a timeHalf-filled pencil marks produce false deductions, because a digit you have not written down looks eliminated. Fill every square of a run, or none of them, and let the crossings do the erasing.
Common questions about kakuro
- What does the diagonal line in a kakuro cell mean?
- It separates two clues. The number above the line is the total for the white squares running right from that cell; the number below the line is the total for the squares running down from it. A cell may carry one, both or neither.
- How long can a run be in kakuro?
- Between two and nine squares. One square is not a run at all, and ten would need ten different digits, which do not exist — there are only nine to choose from.
- Is kakuro just arithmetic?
- Barely. After a few grids you stop adding and start recognising clues as sets of digits. The puzzle is logic about which set goes where, and the addition is a lookup you do once and then remember.
- What is the easiest clue in kakuro?
- A nine-square run. It can only total 45 and must contain every digit from 1 to 9, so the whole run is known the moment you count its squares. An eight-square run is nearly as generous.
Ready to stop reading? Play kakuro on the full board, with controls and statistics tailored to that game.