Variants
Meet Kakuro
An introduction to Kakuro — what it is, how it differs from Sudoku, and why people who like number-logic puzzles often end up preferring it.
Kakuro is the other big number-logic puzzle. Like Sudoku, it uses digits 1 through 9 and a fill-in-the-grid format. Unlike Sudoku, the grid is shaped more like a crossword than a square block, and the rules are about sums rather than rows-columns-and-boxes.
If classic Sudoku is the world's most famous logic puzzle, Kakuro is the one its enthusiasts often graduate to. Some people who never click with Sudoku take to Kakuro on their first puzzle. Others bounce off Kakuro and stay on Sudoku forever. The difference is mostly in the kind of constraint your brain finds satisfying.
How Kakuro differs from Sudoku
The grid is laid out like a crossword. Black squares divide the grid into runs of white squares, and each run has a target sum displayed at its start in a triangular split-box, like a crossword clue. The rules:
- Fill every white square with a digit from 1 to 9.
- Each horizontal run must add up to the sum displayed at its left end, with no repeated digits inside the run.
- Each vertical run must add up to the sum displayed at its top, with no repeated digits inside the run.
That's it. There's no 3×3 box rule, no row-of-nine constraint, no fixed grid size. Kakuro grids range from small 5×5 starters to 15×15 monsters. The arithmetic is the puzzle.
How the experience differs
Sudoku is mostly visual. You scan rows and columns and boxes, your eye finds patterns, and the placement happens once the constraints have lined up. Pencil marks track candidates, but most easy and medium moves are visible without writing anything down.
Kakuro is mostly arithmetic. Each run has a small library of valid digit combinations — a three-cell run summing to 6 must be 1+2+3 (only combination); a two-cell run summing to 17 must be 8+9 (only pair). Solving Kakuro is largely about identifying these constrained runs, intersecting their possible digits with the constraints from crossing runs, and narrowing each cell's options that way.
The arithmetic isn't hard — every Kakuro can be solved with single-digit addition — but the satisfaction is different from Sudoku's. Where Sudoku says "this cell can only hold this digit because the digit is needed elsewhere," Kakuro says "this cell can only hold this digit because nothing else makes the sum work."
The other shift is grid size. Sudoku is fixed at 9×9, while Kakuro grids vary considerably — from 5×5 starters that finish in five minutes to 15×15 expert puzzles that can take an hour or more. The longer puzzles are a different cognitive shape from any Sudoku, requiring you to hold a larger problem space in your head while working a single run.
Where to start
Kakuro's beginner cliff is steeper than Sudoku's. The combinatorics aren't intuitive at first — you have to learn that two-cell runs summing to 17 are uniquely 8+9, that three-cell runs summing to 7 are uniquely 1+2+4, and so on. There's a small cheat-sheet of "essential combinations" that most beginners refer to for their first ten or so puzzles before the patterns become habit.
If you're starting from zero, our Kakuro easy puzzles at 5×5 are the right starting point — small enough to finish in five or ten minutes, long enough to surface the recurring combinations you'll need to recognise. Don't expect speed on the first one; expect the same gradual pattern recognition any puzzle requires.
The honest summary: Kakuro and Sudoku are cousins, not the same puzzle. Some solvers find Sudoku's elegance more pleasant than Kakuro's arithmetic; others find Kakuro's combinations more satisfying than Sudoku's pattern recognition. Trying one Kakuro puzzle costs nothing, and the verdict comes quickly. If it clicks, you've found a new puzzle to fold into your day.
Related reading
Rules & basics
How to Play Sudoku: The Complete Beginner's Guide
Learn the rules of Sudoku, the core solving moves, and the habits that take a beginner from confused to confident in a single afternoon.
4 min read
Variants
Meet Killer Sudoku
An introduction to Killer Sudoku for someone who knows the classic version — what changes, how the experience differs, and where to start.
4 min read
Techniques
The two moves that solve most easy puzzles
The naked single and the hidden single — the two foundational Sudoku moves, what each one looks like, and the perspective shift between them.
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Glossary terms
- Kakuro— A Japanese number-placement puzzle. Cross-sums act like a crossword grid; players fill white cells with digits 1–9 so each run sums to its target without repeating a digit.
- Run (kakuro)— A horizontal or vertical sum-segment in a kakuro grid. The white cells from one clue cell to the next, which must sum to the clue's target without repeating a digit.
- Clue cell— The dark cell in a kakuro grid carrying the target sums for the runs extending from it — usually one or two numbers separated by a slash.
- Entry cell— A white cell in a kakuro grid that the player fills with a digit. Each entry cell belongs to exactly two runs — one horizontal, one vertical — and must satisfy both.
- Kakuro sum combinations— The reference table mapping each (cell-count, target-sum) pair to its valid digit combinations. The foundational lookup that anchors most kakuro deduction.
- Unique sum— A kakuro run whose cell count and target sum together force exactly one valid digit combination — the most direct deductive move in the puzzle.
- Cross-reference— Kakuro deduction at the intersection of two runs. The cell shared between a row run and a column run must hold a digit valid in both — usually pinning the cell directly.
- Kakuro pair— Two cells in a kakuro run sharing the same two-digit possible set. The two digits are confined to those two cells, eliminating them from every other cell of the run.