Kakuro Online

What is Kakuro?

Kakuro is often described as a number crossword because its clues behave like crossword entries, but the answers are sums rather than words. A dark clue cell points to one uninterrupted horizontal or vertical run of white cells. Fill those white cells with digits from 1 through 9 so their total equals the clue. There is one extra rule that drives most of the deduction: a digit cannot repeat inside the same run.

Suppose a two-cell run totals 3. Because the two digits must be different, the only possible set is 1 and 2. A two-cell run totaling 17 can only be 8 and 9. Those extreme sums are immediately restrictive. Middle totals usually allow several combinations, so you have to combine the clue with the crossing run at each cell. A cell belongs to one Across run and one Down run; its value must satisfy both at once.

That crossing structure is why Kakuro is more than repeated addition. You may know that an Across run can use 2, 4 and 7 in some order, while the selected cell’s Down run allows only 1, 4 or 9. Their intersection leaves 4. A good solve repeatedly narrows these intersections, updates remaining totals and removes digits already used in the run.

Unique solutions are verified, not assumed

Generating a filled number grid and adding sums is easy. Proving that the clues force exactly one answer is not. The V0.78 source builder constructs candidate boards, derives all Across and Down runs, then sends each candidate to a separate solution-counting solver. The solver enumerates legal ordered digit permutations for every sum, propagates crossing values and stops after finding a second solution. A source enters the committed bank only when that independent solver finds exactly one solution and that solution matches the generated answer.

The committed bank contains 20 Easy sources, 20 Standard sources and 14 Hard sources. Practice then applies one of eight reflection or rotation transforms to the playable interior. The clues are recalculated after the transform rather than copied as decorative text. Because a symmetry transform preserves the constraint graph, each transformed board remains mathematically equivalent to its verified source. That produces 432 reproducible source-and-transform combinations without pretending that superficial randomization creates new proof.

Easy, Standard and Hard are different solving workloads

Easy uses compact 6×6 source boards with a smaller white-cell workload and deliberately restrictive sums. This makes it easier to learn how combination sets work and to see the effect of one crossing clue on another. It is a useful first stop if you are new to Kakuro or want a shorter number-logic session.

Standard uses 7×7 boards and a broader spread of clue combinations. More cells can remain plausible for longer, so the selected-run panel becomes useful for checking what a clue still permits after a few entries. Standard is the default because it balances visible deduction with enough depth for repeat play.

Hard keeps a bounded 7×7 format but favors denser accepted layouts and broader combination possibilities. The goal is not to call a board hard merely because it is physically larger. Hard should create more interacting unresolved runs while still remaining practical on a phone and still passing the same exact uniqueness gate.

Tools that expose constraints without silently solving the board

Select any white cell and the side panel shows its Across and Down clues, the amount already entered, the amount remaining and legal digit sets consistent with current values. Those combination chips are a study aid: they show what a run can still contain, but they do not assign the digits to exact cells. The cell-level candidate line intersects both crossing runs so you can see which digits remain legal at that location.

Notes mode lets you maintain pencil marks manually. Auto Notes recalculates candidates from both crossing runs for every empty cell. Undo and Redo make experimentation reversible. Live conflict highlighting catches repeated digits or a run that can no longer reach its clue with any legal combination. These checks are based on the puzzle rules, not on peeking at the final answer.

The explicit Check action is different. Check compares entered values with the frozen unique solution and therefore marks the attempt assisted if it finds an error. Hint fills one answer and also makes the solve assisted. Clean personal bests require no Hint and no checked mistake. That distinction keeps ordinary constraint tools available for learning while keeping a stricter local record for fully independent solves.

Autosave, Daily play and print

Unlimited Practice stores the exact difficulty, source, transform, entered values, notes, elapsed time and assistance state in local browser storage. Reloading the same puzzle resumes it instead of swapping in a different board. Fresh generates a new seeded Practice identity. No account or server database is required for that persistence.

Daily Kakuro selects one date-stable verified source and transform and keeps a separate browser-local Daily history and streak. It is intentionally a specialist Daily, not a thirteenth game in the platform’s frozen Today’s 6 system. The Today’s 6 lineup is not changed by adding Kakuro to the Practice catalog.

The Print control uses a paper-focused layout that removes navigation and play controls while keeping the grid and clues. It is intended for solving the same generated board away from the screen; it does not create a separate family of thin printable landing pages.

What Kakuro practices

Kakuro repeatedly combines small-number arithmetic with constraint reasoning. You estimate remaining totals, recognize restrictive digit combinations, track exclusions within a run and coordinate two crossing conditions at every cell. That can make it a useful arithmetic-fluency and logic exercise, but the site deliberately avoids turning completion time into an IQ claim, school grade or population percentile.

The score is a local game metric. Completion matters first, with a modest time component and transparent penalties for Hint or checked mistakes. Clean personal bests are stored by difficulty in this browser. There is no fake global leaderboard and no claim that a local best represents how you rank against other players.

How to start

If the clue notation is unfamiliar, start with Easy and select a white cell before entering anything. Read both crossing run cards, note the possible digit sets and look for a clue with only one or two combinations. When one digit becomes forced, enter it and inspect how the crossing run changes. Move to Standard when you are comfortable deriving candidates from two sums rather than treating each clue separately.