Kakuro online

Cross sums to play or print

This kakuro online tool gives you puzzles of 6 × 6, 8 × 8, 10 × 10 and 12 × 12 cells in three levels. Every puzzle has exactly one solution, checked before it appears on screen. You can play with a mouse, a finger or the keyboard, use pencil marks, a combination helper and a timer, then print the puzzle on A4 with the solution on a second page.

Kakuro is also known as cross sums. Think of a crossword where the words are replaced by numbers: light mental arithmetic, a lot of logic, and a good fit for a commute or a lunch break.

How kakuro works

The grid mixes black and white cells. White cells in a line form runs, across or down. Each run starts after a black cell split by a diagonal: the number in the top right is the sum of the run going right, the number in the bottom left is the sum of the run going down.

• Write a digit from 1 to 9 in every white cell (never 0).
• The digits of a run add up to the clue exactly.
• A digit cannot appear twice in the same run.

A small example on a square of four cells. The top run is 3 in 2 cells, the left run is 4 in 2 cells, the bottom run is 12 and the right run is 11. 3 in 2 can only be 1 + 2. 4 in 2 can only be 1 + 3, because 2 + 2 repeats a digit. The top left cell belongs to both runs, so it holds the shared digit, 1. That puts 2 in the top right and 3 in the bottom left. The bottom run is 12, so the last cell is 9, and the right run checks out: 2 + 9 = 11.

How to play

1. Pick a size from “6 × 6” to “12 × 12”, then a level. The size includes the first row and first column, which are always black, so an 8 × 8 puzzle has at most 7 × 7 cells to fill.
2. Tap a white cell, then a digit on the pad, or type it. The arrow keys jump from one white cell to the next.
3. “Notes” (or the N key) adds small candidate digits. A digit you place is removed from the notes of both its runs.
4. The “Possible combinations” box shows, for the selected cell, both sums, all their combinations and the digits that fit both at once. A struck-out combination no longer matches the digits already placed.
5. “Show mistakes” turns wrong digits red. “Hint” fills the selected cell, or another empty or wrong cell. “Undo”, “Redo” and “Restart” do what they say.

The “Puzzle number” goes from 1 to 999,999. Same size, same level and same number give exactly the same puzzle, which is handy for challenging a friend or comparing times at the office.

Combinations worth knowing by heart

Some sums can only be made one way. Spotting them gives you the first safe cells.

Two more shortcuts: a run of 8 cells misses exactly one digit, equal to 45 minus the sum (an 8-cell run of 39 has no 6). A run of 9 cells always adds up to 45. The “Combination table” below the grid lists every way to make a sum without a puzzle: 15 in 2 cells gives 6 + 9 and 7 + 8.

Solving techniques

The shared digit

Each white cell sits on one across run and one down run. If one is 16 in 2 (7 or 9) and the other is 24 in 3 (7, 8 or 9), the cell is 7 or 9. If the down run is 23 in 3 (6, 8 or 9) instead, the cell can only be 9.

Ruled-out digits

An even sum in two cells never uses its half: 14 in 2 cells never contains 7, 6 in 2 cells never contains 3. 6 in 2 also rules out 6 to 9, since the partner would be 0 or less.

Bounds

Take a run of 19 in 3 cells where one cell crosses a 4 in 2 run, so it is 1 or 3. With 1, the other two would need 18, but 8 + 9 = 17 at most. The cell is therefore 3, and the other two make 16: 7 and 9.

Pencil marks

On large grids, note the candidates of cells that cross two rare sums, then cross them out as you go.

Printing a puzzle

“Print (puzzle and solution)” prepares two A4 pages: the empty grid with its sums and number, then the filled grid. Black cells print in light grey to save ink. For a classroom or a puzzle club, print only the first page.

Frequently asked questions

Can a puzzle have two solutions?

No. Before a puzzle appears, a solver looks for a second solution by trying every combination of every sum. All puzzles can be solved by deduction, without guessing.

Can the same digit appear twice?

Not in the same run. A digit can come back elsewhere in the grid, even twice on one row if a black cell separates the two runs.

Is my game saved if I close the page?

Yes. The puzzle, your digits, your notes and the time stay on this device and nothing is sent. The timer stops while the page is hidden.

What changes between levels?

The level sets the length of the runs and the share of black cells. On “Easy”, no run is longer than 4 cells; on “Medium”, 6 cells; on “Hard”, 8 cells, with fewer black cells. The longer a run, the more combinations it allows.