How to play Kakuro

Kakuro is a crossword with numbers. You fill the white cells with digits, and each row or column of cells must add up to its clue.

What is Kakuro?

Kakuro is a logic puzzle with sums. In the US, puzzle magazines call it "cross sums". The name Kakuro comes from Japan. It is short for "kasan kurosu", which means "addition cross".

You need only simple addition. You never need to guess: a good Kakuro has one solution, and you find it with logic.

The rules

Put one digit from 1 to 9 in each white cell.
A line of white cells across or down is a run. Each run starts next to a clue cell.
The number in the top right of a clue cell is the sum of the run to its right. The number in the bottom left is the sum of the run below it.
The digits in a run must add up to its clue.
A run never uses the same digit twice. For example, a clue of 4 in two cells is 1 + 3, never 2 + 2.

A worked example

This small puzzle has two runs across and three runs down. Try it first, then read the steps.

	9	4	12
6
19

The puzzle. Across clues: 6 and 19. Down clues: 9, 4 and 12.

Step 1: the top row is 1, 2 and 3

The top run has 3 cells and a clue of 6. Three different digits that add up to 6 must be 1, 2 and 3. No other set works. So each top cell holds 1, 2 or 3.

Step 2: the middle column is 1 and 3

The middle column has 2 cells and a clue of 4. Two different digits that make 4 are 1 and 3. (2 + 2 repeats a digit.)

	9	4	12
6	1 2 3	1 3	1 2 3
19		1 3

The small digits show what each cell can still hold.

Step 3: the right column is 3 and 9

The right column adds up to 12. Its top cell is 1, 2 or 3, so the bottom cell is 11, 10 or 9. A cell holds only one digit, so the bottom cell is 9 and the top cell is 3.

	9	4	12
6			3
19			9

The 12 clue fixes both cells of the right column.

Step 4: finish the grid

The top row already has 3. The middle top cell is 1 or 3, so it is 1. The middle bottom cell is then 3 (1 + 3 = 4).
The top row needs 6, so the left top cell is 6 − 1 − 3 = 2.
The left column needs 9, so the left bottom cell is 9 − 2 = 7.
Check the bottom row: 7 + 3 + 9 = 19. It works.

	9	4	12
6	2	1	3
19	7	3	9

The solution. Every run adds up, and no run repeats a digit.

Tips for your first puzzles

Start with the clues that have only one set of digits. Examples are 3 or 4 in two cells, and 6 or 24 in three cells. The Kakuro combinations chart lists all of them.
Look where an across run and a down run cross. The cell can hold only a digit that both runs allow.
Write small notes of the digits a cell can hold, and remove them as you go.
For more methods, read how to solve Kakuro.

Play Kakuro on iPhone

Cross Sums has free daily Kakuro and Calcudoku puzzles, a short tutorial and hints that explain the next step. See the app.