Kakuro Solver

Copy a Kakuro from a puzzle book or newspaper onto the grid to find out whether it has exactly one answer, see the full solution, or reveal one cell at a time with the rule that decides it. The combination table lists which digits can make a given sum.

How to use

1. Choose "Rows" and "Columns" (3 to 16) so the grid matches the puzzle, including the black cells along the top and left edges. To try the tool first, press "Small example 5×5" or "Medium example 9×8".
2. Tap a cell and press "Make black" or "Make white". On a black cell choose "→ across sum" or "↓ down sum" and type the number on the keypad; up to two digits are kept. Digits already written in white cells can be entered too.
3. Read the message under the grid. It names a run without a sum, an impossible sum (for example 25 in two cells) or a repeated digit, and marks the cells in red.
4. Press "Solve". The answer appears in blue and the message says whether it is unique. "Hide answer" removes it again, and "Hint: one cell" fills a single cell in green with the reason.
5. "Save as PNG" downloads the grid as it is shown, with or without the answer. "Clear all" empties the board.

How it works

• The solver keeps a set of possible digits for every white cell, removes digits that fit no combination of the run, and tries values in the cell with the fewest possibilities when the rules stall. It keeps searching after the first answer; finding a second one means the puzzle as entered is not unique. A search stops after 10 seconds.
• Hints use three rules in this order: the last empty cell of a run, a run with only one possible digit set where the digit has a single place, and crossing runs that leave one digit. When none of them applies, one cell is taken from the solution and the message says so.
• The board, the answer and the hints are kept in this browser only.

Kakuro rules

Every white cell holds a digit from 1 to 9. A black cell with a number is a clue: the number above the diagonal is the sum of the white cells to its right up to the next black cell, the number below the diagonal is the sum of the white cells under it. Such a line of white cells is called a run, and a digit cannot repeat within a run.

Solving Kakuro by hand

Start with sums that have only one combination. Two cells adding to 3 must be 1 and 2, two cells adding to 17 must be 8 and 9, three cells adding to 6 must be 1, 2 and 3, and three cells adding to 24 must be 7, 8 and 9. The combination table on this page shows every such case; enter the number of cells and the sum.

Then look where two runs cross. The crossing cell must use a digit that belongs to both runs' combinations. For example, if the across run is 1 and 2 and the down run is two cells adding to 4 (1 and 3), the crossing cell is 1. Finish with the last cell of a run: once all but one cell are known, the missing digit is the sum minus the others.

Questions and answers

What if the solver finds more than one answer?

A published Kakuro has exactly one answer, so several answers almost always mean an input mistake: a missing sum, a sum in the wrong half of a clue cell, or a black cell in the wrong place. One possible answer is shown so that you can compare it with the paper.

What does a Kakuro combination table show?

For a number of cells and a sum it lists every set of different digits 1 to 9 that adds up to it. Two cells adding to 10 have four sets: 1 9, 2 8, 3 7 and 4 6. The full table covers 2 to 9 cells.

Why does it say a sum is impossible?

Different digits limit the range of a run: two cells give 3 to 17, three cells 6 to 24, nine cells exactly 45. A sum outside that range is usually a misread digit or a run that should be longer.

Can I see one cell at a time instead of the whole answer?

Yes. "Hint: one cell" fills only one cell and explains the rule. Press it again for the next one; the full answer stays hidden until you press "Show answer" or "Solve".