How to Play Kakuro
Kakuro is often called a mathematical crossword: instead of filling white squares with letters, you fill them with digits so that each run of squares adds up to its clue. If you enjoy Sudoku but want a puzzle where arithmetic and logic meet, Kakuro is the perfect next step. It looks intimidating, but a handful of reliable techniques will get you solving quickly.
The Objective
Fill every white cell with a digit from 1 to 9 so that:
- Each horizontal run sums to the clue in the black cell to its left (shown in the upper-right triangle).
- Each vertical run sums to the clue in the black cell above it (shown in the lower-left triangle).
- No digit repeats within a single run.
That no-repeat rule is what makes Kakuro solvable by pure logic rather than guesswork.
Reading the Board
- A black cell can carry two clues: a number in the top-right is the total for the row running to its right; a number in the bottom-left is the total for the column running below it.
- A "run" is an unbroken line of white cells between black cells. Each run has exactly one clue.
- Because digits can't repeat in a run, a run can be at most 9 cells long.
The Key Techniques
Strong Kakuro play is about narrowing down which digits can possibly go where.
- Learn the magic combinations. Some totals have only one possible set of digits. A two-cell run of 3 must be 1+2; a 4 must be 1+3; a 16 must be 7+9; a 17 must be 8+9. Three-cell runs of 6 (1+2+3), 7, 23, and 24 are also unique. Fill these first — they anchor everything around them.
- Use the intersection trick. Every white cell belongs to both a horizontal and a vertical run. The digit there must appear in a valid combination for both runs. Cross off any candidate that can't satisfy both, and often only one digit survives.
- Attack low and high totals. A long run with a small total is forced to use small digits; a long run with a large total is forced to use large ones. These are the most constrained runs — start there.
- Watch the "missing digit." If a run needs a set of digits and all but one cell is filled, the last cell is simply the total minus what's already placed.
- Use pencil notes. Jot every candidate for a cell in small print, then eliminate as intersections tighten. Clearing candidates one by one is far safer than guessing.
A Solving Routine
Start by filling all the unique magic-combination runs. Then walk the intersections: for each open cell, list the candidates allowed by its row combination, and keep only those also allowed by its column. Repeat, and the puzzle unravels one forced digit at a time. Because a proper Kakuro has a single unique solution, you should never need to guess — if you're stuck, there's always a logical deduction waiting.
If you love this kind of pure deduction, try Nonogram for picture logic or Hashi — Bridges for a networked twist.
Sharpen your number sense — Play Kakuro free, then explore more guides.