Kakuro Game
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
What Is Kakuro?
Kakuro is a logic-based number puzzle played on a grid of black and white cells. White cells are filled with digits from 1 to 9. Black cells either act as spacers or contain clue numbers — the clue for a horizontal run (across) appears in the upper-right corner of the black cell, while the clue for a vertical run (down) appears in the lower-left corner. The diagonal slash divides these two triangles visually. Each run of consecutive white cells must contain unique digits (no repetition within the run) that sum exactly to the clue value. Every Kakuro puzzle has a unique solution derivable by logic alone.
How Do the Rules Work?
The key constraint is the combination of sum and uniqueness. Given a run of length L summing to T, only certain digit sets are possible. The minimum possible sum for a run of length L is 1+2+…+L; the maximum is (10-L)+(10-L+1)+…+9. Any run with a sum outside this range has no solution. Within the valid range, the valid digit combinations can be enumerated — this is what the combination helper shows you. To solve a puzzle, you intersect the possible digit sets for across and down runs to narrow down which digits can go in each cell. When only one option remains for a cell, that cell is solved. Continue until all cells are filled.
Why Play Kakuro?
Kakuro exercises both arithmetic and logical deduction simultaneously. Unlike a calculator task, Kakuro is not about computation speed — it is about constraint propagation: using what you know to limit what is possible until the answer is forced. This kind of thinking is directly analogous to skills used in programming, mathematics, and analytical problem-solving. Regularly playing Kakuro has been associated with improved numerical fluency, working memory, and pattern recognition. It is also a deeply satisfying experience: the moment of insight when a run suddenly becomes forced is one of the most rewarding in all of puzzle gaming.
Tips for Beginners
Start with the forced combinations — runs that have only one possible digit set. A 2-cell run summing to 3 must be {1,2}; summing to 17 must be {8,9}. A 3-cell run summing to 6 must be {1,2,3}; summing to 24 must be {7,8,9}. Next, look for cells that appear in two runs: if the across run can only contain {1,3} and the down run can only contain {1,5,9}, the intersection tells you the cell must hold 1. Use pencil marks to track candidates and eliminate them as you solve neighboring cells. Don't guess — Kakuro always has a logical path to the solution. Click any clue cell to open the combination helper and see all valid digit sets instantly.
How to Play Kakuro
Select a Puzzle
Click 'New Game' to open the puzzle selector. Choose from Easy (5×5 or 6×6), Medium (7×7), or Hard (9×9) puzzles. The difficulty controls the number of cells and how many forced combinations appear.
Understand the Grid
Black cells with a diagonal slash are clue cells. The number in the upper-right is the sum for the cells to the right (across run). The number in the lower-left is the sum for the cells below (down run). Click a clue cell at any time to see all valid digit combinations for that run.
Fill White Cells
Click a white cell to select it, then press a digit key (1-9) or tap the on-screen number pad. Each digit must be unique within its horizontal and vertical run and must help the run total equal its clue. Use Pencil mode (P key) to enter candidate notes. Use Check to highlight errors in red.
Complete the Puzzle
When all white cells are filled correctly, the puzzle auto-completes and shows your solve time and hint count. Use Undo (Ctrl+Z) to backtrack, and Hint (when a cell is selected) to reveal a single correct digit if you get stuck. Arrow keys move between cells; the timer pauses if needed.
Frequently Asked Questions
What is the difference between Kakuro and Sudoku?
Sudoku and Kakuro share a grid format and the constraint that digits must not repeat within a group, but they differ fundamentally in how groups are defined and what the constraint is. In Sudoku, digits 1-9 must each appear exactly once in every row, column, and 3×3 box — the constraint is completeness. In Kakuro, each run (any length from 2 to 9 cells) must contain unique digits that sum to a specific target — the constraint is arithmetic. Kakuro runs vary in length, which creates far more varied combinatorial challenges. Kakuro also has no equivalent to Sudoku's box constraint, relying instead entirely on the sum targets and the no-repetition rule.
Are there combinations I should memorize?
Yes — experienced solvers memorize the 'forced' combinations where only one digit set is possible. The most important are: 2-cell runs: sum 3 = {1,2}, sum 4 = {1,3}, sum 16 = {7,9}, sum 17 = {8,9}. Three-cell runs: sum 6 = {1,2,3}, sum 7 = {1,2,4}, sum 23 = {6,8,9}, sum 24 = {7,8,9}. Four-cell runs: sum 10 = {1,2,3,4}, sum 30 = {6,7,8,9}. Five-cell runs: sum 15 = {1,2,3,4,5}, sum 35 = {5,6,7,8,9}. These give you immediate certainty about which digits go in those cells, which then constrains intersecting runs and often unlocks much of the puzzle.
What does the combination helper show?
When you click a clue cell in the grid, the combination helper popup appears and lists every valid digit set for that run — meaning every subset of unique digits from 1-9 that has the correct length and sums to the clue value. For example, a 3-cell run summing to 16 has six valid combinations: {1,6,9}, {2,5,9}, {2,6,8}, {3,4,9}, {3,5,8}, and {4,5,7}. By comparing the valid sets for the across run and the down run through a cell, you can intersect them to determine which digits are possible for that cell. The helper is your best tool for quickly seeing what is constrained.
How do pencil marks work?
Pencil marks (also called candidates) are small digit notes you can write inside a cell when you are not yet certain of the final answer. Toggle pencil mode with the P key or the Pencil button in the toolbar. In pencil mode, pressing a digit toggles it on or off as a candidate — it appears as a small number in the cell's 3×3 micro-grid. When you have narrowed down a cell to a single candidate, switch back to pen mode and enter the final digit. Entering a digit in pen mode automatically clears all pencil marks in that cell. Pencil marks are essential for solving medium and hard puzzles efficiently.
Is there always a unique solution?
All well-formed Kakuro puzzles have exactly one solution. This is a defining property of properly constructed Kakuro puzzles — the combination of all run sum constraints and the no-repetition rule is designed to uniquely determine every cell. If a puzzle has multiple solutions, it is considered malformed. All six built-in puzzles in this game have been manually verified to have exactly one solution. You should never need to guess: if you appear to have two equally valid options, re-examine your combination analysis — one path will be eliminated by considering the intersecting run constraints more carefully.
What do the keyboard shortcuts do?
This game is fully keyboard-accessible. After clicking a white cell to select it, use the digit keys 1-9 to enter values, and Backspace, Delete, or 0 to clear. Arrow keys move the selection to the nearest white cell in that direction, skipping over black and clue cells. P toggles between pen and pencil mode. Ctrl+Z undoes the last move; Ctrl+Y or Ctrl+Shift+Z redoes. The timer pauses when you use the pause button. On mobile, the on-screen number pad at the bottom of the right panel provides tap access to all digits and the erase button.