Kakuro Rules: How to Play (With a Printable Example)

Kakuro is often described as a crossword made of numbers. These are the Kakuro rules exactly as they apply in a LogikLand grid, followed by a complete solution of a small grid so you can see every rule at work.

What Kakuro is

A Kakuro grid has white cells, where you write digits, and grey cells that carry clues. A row or column of white cells between two grey cells is called a run. Each run has a target sum written in the grey cell that comes just before it. You fill every white cell so that every run adds up to its target.

How to read a clue cell

A grey cell is cut by a diagonal line. The number in the top right corner is the sum of the run that starts to its right. The number in the bottom left corner is the sum of the run that goes down from it. A grey cell with one number has only one run. In LogikLand grids the first row and the first column are always grey, because they carry the clues of the first runs.

The rules

1. Write a digit from 1 to 9 in every white cell.
2. The digits of a run add up to the number of its clue.
3. A digit cannot be used twice in the same run.
4. A white cell belongs to two runs, one across and one down, and must satisfy both.
5. The same digit may appear again in a different run.

A worked example

Here is an easy LogikLand grid with its solution. The play area is 6 by 6 cells, with the clue row and clue column on top. We will solve two corners of it with logic only.

The top left corner

1. Row 1 starts with a clue of 3 over two cells. Only 1 + 2 makes 3, so these two cells hold 1 and 2.
2. The column under the clue 6 has two cells, and its top cell is the 1 or the 2 from step 1. The pairs that make 6 with a 1 or 2 are 1 + 5 and 2 + 4. So the cell below holds 5 or 4.
3. Row 2 starts with a clue of 14 over two cells. A pair that makes 14 uses at least a 5 (5 + 9 or 6 + 8), so the cell on the left cannot be 4. It is 5.
4. With 5 below, the top cell of that column is 1 (1 + 5 = 6), the cell next to it in row 1 is 2, and the other cell of row 2 is 14 − 5 = 9.

The bottom left corner

1. The column with clue 17 over two cells needs 8 + 9. The same is true for the column and the row that carry 17 further right.
2. The last row starts with 23 over three cells. The only three different digits with that sum are 6, 8 and 9. Its first column has a clue of 12 over two cells, so its bottom cell is 8 or 9 (12 − 8 = 4 and 12 − 9 = 3 are fine, 12 − 6 = 6 is a repeat).
3. Two of the three cells of the last row are therefore 8 and 9, so the remaining one, which belongs to the tall column of clue 30, is 6.
4. The row above has clue 20 over three cells. Try the bottom row as 8, 9, 6. The cells above the 8 and the 9 are then 12 − 8 = 4 and 17 − 9 = 8, and the third cell of that row would be 20 − 4 − 8 = 8, a repeat of the 8 in the same run. That is forbidden. So the bottom row is 9, 8, 6, the cells above are 3 and 9, and the third one is 20 − 3 − 9 = 8.

Every other cell of the grid follows in the same way, one run at a time.

Sums that have only one answer

Some sums can only be made with one set of digits. Learn these and many runs solve themselves.

The order of the digits inside the run is not given by the clue. Only the set is. The crossing runs decide the order.

Grid sizes in LogikLand

The Kakuro assistant offers four levels. The size counts the white area, without the clue row and column.

Runs are never shorter than 2 cells. Longer runs of 9 cells are not used, because such grids almost never have a single solution.

Making a Kakuro book

There is no free single-grid Kakuro tool on LogikLand. Books are made in the Kakuro assistant, which you reach after you create a free account. You can put 1 or 2 grids on a page (only 1 in a 6 x 9 book that has hard or expert grids, where the clue numbers would be too small) and 1, 2, 4 or 6 solutions per page. Our suggestion, not a rule: start with an easy grid on paper to check that the digits are big enough for your readers.

Questions