The number crossword puzzle — fill each run with unique digits that sum to the clue

Kakuro is one of the most satisfying and intellectually rewarding number puzzles in the world. Often described as a number crossword, it combines the familiar black-and-white grid structure of a crossword puzzle with the arithmetic challenge of placing the right digits in the right cells. Unlike Sudoku, which is purely about arrangement, Kakuro requires you to think numerically — every answer must not only be unique within its run but must also sum to a specific target value shown in the clue cell. This combination of constraints makes each puzzle a uniquely satisfying logical deduction exercise. The rules of Kakuro are elegantly simple yet lead to deep complexity. You fill white answer cells with digits from 1 to 9. No digit may be repeated within a single horizontal or vertical run — a group of consecutive white cells in the same row or column, bounded on both ends by a black or clue cell. Each run has a corresponding clue number shown in the adjacent black cell: the clue appears in the upper-right triangle for an across run (cells to the right) and in the lower-left triangle for a down run (cells below). Every run's digits must sum exactly to its clue value. A well-formed Kakuro puzzle has exactly one valid solution that can always be reached by pure logical deduction without guessing. This free online Kakuro game includes six hand-crafted puzzles spanning easy 5×5 grids suitable for beginners all the way to challenging 9×9 grids for experienced solvers. The interface supports pencil marks for candidates, an undo/redo history, a combination helper that shows every valid digit set for any selected run, hints that reveal a single correct digit, and automatic completion detection with a celebration modal showing your solve time. Kakuro has a rich history stretching back to Japan in the 1980s, though it was first published in the United States under the name 'Cross Sums' in Dell Magazines as far back as 1966. The Japanese puzzle publisher Nikoli popularized it under the name Kakuro — derived from 'kasan kurosu' (addition cross) — in 1987, and it spread worldwide through the puzzle boom of the 2000s. Today it is one of the most widely published number puzzles after Sudoku. One of the most powerful tools for Kakuro solving is the concept of forced combinations, sometimes called 'magic blocks'. When a run has very few valid digit sets — or only one — those cells become immediately constrained. For example, a two-cell run summing to 3 can only be {1, 2}; a two-cell run summing to 17 can only be {8, 9}. Similarly, a three-cell run summing to 6 must be {1, 2, 3}, and one summing to 24 must be {7, 8, 9}. Learning to spot these forced combinations quickly is the key skill that separates experienced Kakuro solvers from beginners. Our built-in combination helper shows you all valid digit sets for any run with a single click on the clue cell. The pencil mark (or candidate) system is equally important for harder puzzles. When you are not yet certain which digit goes in a particular cell, you can enter small candidate digits in pencil mode — up to all nine digits in a 3×3 micro-grid within each cell. As you solve other cells in the same run, you eliminate candidates until only one remains. The pencil mode toggle switches between full digit entry (pen mode) and candidate entry (pencil mode), and you can switch instantly with the P key. Progress is auto-saved to your browser's local storage, so you can close the tab and resume your puzzle exactly where you left off. The timer starts on your first move and can be paused at any time. The Check button highlights any incorrectly placed digits in red without revealing the correct values, letting you know where to focus your attention. The Hint button fills in the correct digit for the currently selected cell and increments a hint counter shown in the toolbar.

Understanding Kakuro

How to Play Kakuro

Frequently Asked Questions