This kakuro solver takes the puzzle you are stuck on, not a puzzle of the day. Set the grid size, mark the black clue cells, type each down and across sum, and press Solve. The solver fills every white cell and tells you whether the answer is the only one. Press Next step instead to place one digit at a time, with the reason written out.
How to enter a kakuro
- Pick the width and height, counting the clue row along the top and the clue column on the left. A new grid starts with those two lines already black.
- Tap a cell and choose Clue cell to make it black. Type the down sum (the cells below it) and the across sum (the cells to its right). Leave a box empty when that direction has no clue.
- Everything else stays white. If your puzzle prints a digit in a white cell, tap the cell and type it.
On a keyboard you can work without the mouse: arrow keys move, Space switches a cell between black and white, D or A picks the down or across sum, and digits type the number. You can also paste the whole grid as text, one row per line.
The rules
Each run of white cells, across or down, must add up to the clue at its start, using the digits 1 to 9 with no digit twice in the same run. A run of two cells with clue 16 can only be 7 and 9; a run of three with clue 6 can only be 1, 2 and 3. Those forced combinations are where every kakuro starts.
How the solver works
For each run the solver lists every set of different digits that reaches the sum, the same list the combination finder shows. It drops any set that cannot be placed in the cells, given what the crossing runs allow, and keeps narrowing until nothing changes. When logic alone stops, it tries the candidates of the most constrained cell and repeats, and it keeps searching after the first answer to prove there is no second one. If the clues contradict each other, it says so instead of guessing.
The step hints follow the order a person would use: first a cell where the across and down runs share only one digit, then a digit every combination of a run needs that only one cell can take, then deeper cross-checking. On the example puzzles almost every step is found this way; when no simple step exists, the hint says so and gives the digit from the proven solution.
Worked example
Take a 2 by 2 block with across clues 17 (top row) and 8 (bottom row) and down clues 16 (left column) and 9 (right column). Across 17 in two cells can only be 8 + 9, and down 16 in two cells can only be 7 + 9. The top left cell belongs to both runs, so it is the only digit they share: 9. Then the top right cell is 17 minus 9 = 8, the bottom left is 16 minus 9 = 7, and the bottom right is 8 minus 7 = 1, which also gives 8 + 1 = 9 for the right column. Load this as text with the three lines # 16\ 9\, \17 . . and \8 . . to watch the hints do the same thing. If one clue were wrong, say 7 instead of 8 on the bottom row, the solver would report that no solution exists.
Solving tips
- Learn the unique combinations: 3 in 2 is 1+2, 4 in 2 is 1+3, 16 in 2 is 7+9, 17 in 2 is 8+9, 6 in 3 is 1+2+3, 7 in 3 is 1+2+4, 23 in 3 is 6+8+9, 24 in 3 is 7+8+9.
- Look for a cell where a small run crosses a large run: the overlap is often a single digit.
- A digit that every combination of a run contains must go somewhere in that run; if only one cell can take it, place it.
The full chart of sums is on the kakuro combinations page, with a filter for the digits you already know.
Want a grid to play? Kakuro online makes new puzzles at three levels and a daily kakuro.
Solver tested . Found a problem? Tell us.
Questions
Can a kakuro have more than one solution?
A well-made kakuro has exactly one. If you entered a clue wrong, or the puzzle is flawed, the solver shows two different answers and marks the cells where they differ, so you can see which clue to check.
What are the kakuro combinations for a sum?
Use the combination finder next to the grid: type the sum and the number of cells and it lists every set of different digits that works, plus the digits that are always or never used. You can also require or exclude digits.
Why does the solver say there is no solution?
Every way of filling the grid breaks at least one clue. That nearly always means a sum was typed in the wrong cell or the wrong box (down instead of across). The message also catches sums that are impossible on their own, such as 30 in two cells.
How big can the grid be?
Up to 20 by 20 cells. The example and test puzzles, up to 10 by 10, solve in a few milliseconds; the search runs in the background, so the page stays responsive and you can cancel it.
Is kakuro the same as cross sums?
Yes. Kakuro, cross sums and sum puzzles are names for the same puzzle: runs of white cells that must add up to their clue with no repeated digit.