Easy
Short runs with few valid digit combinations. Most moves are forced from the start — the best entry point for learning how sum-and-eliminate logic works.
Free · No account · Unlimited puzzles
Kakuro Puzzles
Kakuro puzzles combine arithmetic and logic in a crossword-style grid. Fill each run of white cells with digits 1–9 so they sum exactly to the clue in the adjacent black cell — without repeating any digit in the same run. Every puzzle has one solution and can be solved by deduction alone.
Free Kakuro generates unlimited puzzles in four difficulty levels, all playable in your browser. No download, no account, no ads.
What are Kakuro puzzles?
A Kakuro puzzle grid is divided into white cells (where you write digits) and black cells (which either block the grid or carry clue numbers). Each clue sits in a black cell at the start of a run — the lower-left triangle holds the down-sum for the vertical run below it, and the upper-right triangle holds the across-sum for the horizontal run to its right.
Your task: fill every white cell with a digit from 1 to 9 so that each run's digits add up to its clue and no digit repeats within the same run. Every valid puzzle has exactly one solution, reachable through logic without any guessing.
Kakuro originated in Japan (where it is called カックロ) and became popular in the United States in the 1980s under the name Cross Sums. Learn the full history at kakuro cross sums.
Kakuro puzzle difficulty levels
Medium
Longer runs and more crossing constraints. You will need to track candidates per cell and eliminate by intersection rather than relying solely on forced combinations.
Hard
Dense grids with heavy overlap between across and down runs. Requires residual-sum reasoning and multi-step cross-run elimination to make consistent progress.
Ultra Hard
Maximum density, long runs, and sparse forced moves. Every available constraint must be used. Intended for solvers who have exhausted hard puzzles and want more.
How to solve Kakuro puzzles
- 1
Find forced combinations
A run with a unique digit set is fully determined before you place anything. Example: a 2-cell run summing to 3 can only be {1, 2}. Check the combination reference for every run before you start writing digits.
- 2
Mark candidates
For each white cell, note which digits from its run's possible combinations are still available after neighboring constraints. The candidate toggle in Free Kakuro displays a 3×3 digit grid inside each cell automatically.
- 3
Apply cross-run intersection
Where an across run and a down run share a cell, the digit must satisfy both. If a digit is not in the candidate set for one run, remove it from the crossing cell. This cascade of eliminations resolves most hard puzzles.
- 4
Use residual sums
Once some cells in a run are filled, recompute the remaining sum for the unfilled cells. A shorter sub-run with a tight target may force new combinations that were not visible at the start.
For a deeper breakdown of each technique — including naked pairs and hidden singles — visit the technique library. If you want a quick lookup for any clue, the Kakuro helper calculator returns all valid digit sets for any sum and run length.
Puzzle tools built into Free Kakuro
Candidate notes
Toggle a 3×3 digit grid inside any white cell to track which values are still possible. Candidates narrow automatically when digits are placed in intersecting runs.
Smart hints
Request a hint at any point. The engine identifies the next forced cell and explains the logic — useful when you want to learn, not just finish.
Auto-play
Advances through all currently forced deductions in one step. Useful for confirming your setup before working the harder cells.
Combination reference
Every valid digit set for every sum–length pair, accessible from the board. No hand-enumeration needed. Full standalone chart at combinations.
Kakuro puzzles vs. Sudoku
Both Kakuro and Sudoku use a no-repeat placement rule, but the logic layer is different. Sudoku constrains placement across rows, columns, and boxes — the arithmetic is trivial (you place 1–9 once each). Kakuro places no global row/column constraint, but adds sum constraints: before you can even think about placement, you must determine which digit combinations are numerically possible for each run.
This means Kakuro rewards pre-solving the combination space before touching the grid, then applying intersection logic to resolve ambiguity. Players who enjoy both puzzles often describe Kakuro as requiring more deliberate front-loaded analysis compared to Sudoku's more iterative row/column scanning.
If you enjoy Kakuro-style number puzzles, you may also like free online Sudoku at RueDoku — or Takuzu (0/1 binary puzzles) at FreeTakuzu.
Which puzzle should you start with?
New to Kakuro: Read the beginner guide, then play an easy puzzle. The forced-move pattern will become obvious within a few cells.
Comfortable with easy: Move to medium difficulty. Keep the combination chart open in a side tab until the common sets are memorized.
Looking for a challenge: Try hard or ultra hard puzzles. Study the technique library for strategies like naked pairs and residual sums.
Want paper puzzles: The printable Kakuro guide walks through printing cleanly from your browser — no PDF required.
Kakuro puzzles FAQ
- What are Kakuro puzzles?
- Kakuro is a number-logic puzzle on a crossword-style grid. Each run of white cells must total the clue in the adjacent black cell, and digits 1–9 cannot repeat in a run. Every puzzle has a unique logical solution.
- Are Kakuro puzzles free to play online?
- Yes. Free Kakuro generates unlimited puzzles at four difficulty levels with no account, no download, and no paywall. Play directly in any modern browser on desktop or mobile.
- How hard are Kakuro puzzles compared to Sudoku?
- Easy Kakuro is roughly comparable to easy Sudoku. Hard and ultra-hard Kakuro can be more demanding because the combination layer adds a front-loaded analysis step that Sudoku does not require.
- Do Kakuro puzzles require math skills?
- Only basic addition. The combination reference handles the arithmetic lookup, so solving Kakuro is primarily about logical elimination rather than mental arithmetic.
- Where can I find printable Kakuro puzzles?
- Use your browser's print function on any puzzle at freekakuro.com, or see the printable Kakuro guide for step-by-step instructions.
- What is the best strategy for solving Kakuro puzzles?
- Start by identifying forced combinations (runs where only one digit set is numerically possible), then resolve ambiguity using cross-run intersection logic. The technique library covers advanced strategies for harder puzzles.