How to play Kakuro

Kakuro is a crossword made of numbers. Instead of words you write digits, and instead of definitions the clues are totals.

The rules

  1. Write a digit from 1 to 9 in every white cell.
  2. Each clue is the total of the run of white cells next to it. The number above the diagonal is for the run going across to its right. The number below the diagonal is for the run going down.
  3. A digit can't appear twice in the same run. It can repeat elsewhere in the row or column, as long as a black cell separates the two.
1220329171682310351544
An easy kakuro. Each black cell with a diagonal holds one or two clues.

Reading the clues

Each black cell can hold two numbers, split by a diagonal line. The number in the top right is the total of the white cells to its right, up to the next black cell or the edge. The number in the bottom left is the total of the white cells below it. So every white cell belongs to exactly two runs: one across and one down.

Your first moves

Look for clues with only one answer

Some totals can only be made one way. Two cells that add up to 3 must be 1 and 2. Two cells that add up to 17 must be 8 and 9. You don't yet know the order, but you know the digits. The techniques guide has the full table.

Cross the runs

A cell sits in an across run and a down run, so its digit has to suit both. If the across run can only use 1 and 2, and the down run can only use 1 and 3, the cell must be 1.

Use small and big totals

A small total means small digits. Two cells that add up to 5 can only use 1, 2, 3 or 4. A big total means big digits: 15 in two cells can only be 6 + 9 or 7 + 8.

Finish runs by subtraction

When a run has one empty cell left, take the digits already there away from the clue. What's left is the answer.

A worked example

416128
A tiny kakuro with four white cells.
  • The down clue 4 covers two cells, so they hold 1 and 3.
  • The down clue 16 covers two cells, so they hold 7 and 9.
  • The top across run adds up to 12. It takes one digit from {1, 3} and one from {7, 9}. Only 3 + 9 makes 12.
  • That leaves 1 and 7 for the bottom row, and 1 + 7 = 8. It checks out.
4161283917
Solved: 3 and 9 on top, 1 and 7 below.

Every kakuro, even a big one, is solved with steps like these. Each new digit makes the next step easier.

1220329171682310351544989736482217213541331
The easy puzzle from above, solved.
Ready? Try today's Kakuro, or read the techniques guide and the full combinations table.

Where kakuro comes from

The puzzle first appeared in the United States as Cross Sums, published by Dell in its puzzle magazines. In the 1980s the Japanese publisher Nikoli picked it up and gave it the name kakuro, short for kasan kurosu, which means "addition cross". It became one of Japan's favourite pencil puzzles, second only to sudoku. After the sudoku craze reached the UK and the rest of the world in 2005, newspapers started printing kakuro too.