How to play Kakuro

Kakuro is often described as a crossword with numbers: instead of words you write digits, and instead of clues you get sums. It rewards careful arithmetic and logic rather than guessing, and every puzzle here has exactly one solution.

The rules

1. Fill every white cell with a digit from 1 to 9.
2. A horizontal block of white cells (an across run) must add up to the number shown in the top-right half of the black cell directly to its left.
3. A vertical block of white cells (a down run) must add up to the number shown in the bottom-left half of the black cell directly above it.
4. A digit may not repeat within a single run. The same digit may appear in different runs.

Every white cell belongs to one across run and one down run. A correctly finished run turns its sum green; a full run with the wrong total or a repeated digit turns it red.

Getting started

Click or tap a white cell to select it, then press a digit on the number pad or your keyboard. Its two runs are highlighted, and the helper panel lists every digit set that fits the across and down sums, striking through sets that conflict with digits already placed. Digits that fit neither run are greyed out on the number pad.

Start with the runs that have only one possible combination. Suppose the cell at row 2, column 3 sits in an across run of two cells with sum 16, and in a down run of three cells with sum 23. Two different digits that add up to 16 can only be 7 and 9. Three different digits that add up to 23 can only be 6, 8 and 9. The only digit in both sets is 9, so that cell must be 9. The other across cell is then 7, and the rest of the down run holds 6 and 8; their crossing runs decide the order.

Use Notes (or press N) to pencil in candidates; a correct digit is removed automatically from the notes in its runs. Arrow keys move the selection.

Strategies and tips

• Learn the unique sums. Some sums have only one combination: 3 in two cells is 1+2, 4 is 1+3, 16 is 7+9 and 17 is 8+9. In three cells, 6 is 1+2+3, 7 is 1+2+4, 23 is 6+8+9 and 24 is 7+8+9. In four cells, 10, 11, 29 and 30 are also fixed. These are your entry points.
• Intersect the sets. A cell must satisfy both of its runs, so only digits common to both candidate lists are possible. This single idea solves most of the grid.
• Look for small and large extremes. A low sum in a long run forces small digits, and a high sum forces large ones. Where a “small” run crosses a “big” run, the shared cell is usually limited to one or two middle values.
• Finish the last cell by subtraction. When all but one cell of a run is filled, the last digit is simply the sum minus the others.
• Use run totals across an area. If a block of cells is covered exactly by some across runs and by some down runs, both groups of sums must match, which can pin down a cell that sticks out.
• Keep errors low. A wrong digit turns red and counts as an error immediately, so check the intersection before you type.

How the difficulty adapts

Your Kakuro rating decides the size of the next grid. New players start at 1800, which gives a 7×7 grid; the five levels range from 5×5 (rating 1000) to 9×9 (rating 2600), and you always get the size closest to your rating. Bigger grids also allow longer runs. A clean solve, finished within the target time for that size and with no more than three errors, adds 80 points. Going over time or making more than three errors costs 160 points, and each hint costs another 80. The rating never drops below 800, and you can jump to any level with the buttons above the board.

The aim is to keep each puzzle a little harder than comfortable. The brain seems to benefit most when the challenge rises along with your skill, so a puzzle that always stretches you is better training than one you can solve on autopilot. You can read more about what research says about puzzles and brain health.

A short history of Kakuro

Sum-based crossword puzzles appeared in American puzzle magazines in the twentieth century, where they were published under the name Cross Sums, most notably by Dell. The Japanese puzzle publisher Nikoli later adopted the format and gave it the name Kakuro, a shortened form of the Japanese words for “addition” and “cross”. In the mid-2000s, following the sudoku craze, Kakuro began to appear in British newspapers and from there spread worldwide.

Frequently asked questions