Kakuro

How to play

Fill every white cell with a digit from 1 to 9. A run is a straight line of white cells, and the grey cell before it carries its total: above the diagonal for the run going right, below it for the run going down.

Every white cell belongs to exactly two runs — one across, one down — and has to satisfy both. There is no zero, and runs are two to nine cells long, so the largest total possible is 45.

And the rule that makes the puzzle solvable: no run repeats a digit. Two cells adding to 4 are 1 and 3, never 2 and 2.

The part that turns arithmetic into deduction

Adding up gets you started. What finishes a puzzle is knowing which totals can be made in only one way, because then the digits are settled even though their order is not — and the crossing runs settle the order.

• Two cells making 3 can only be 1 and 2. Two making 17 can only be 8 and 9.
• Three cells making 7 can only be 1, 2 and 4. Three making 24 can only be 7, 8 and 9.
• Then look at where the runs cross. A cell has to satisfy both of its runs, so the digits it can hold are the ones both allow — and often that is one digit.
• And a combination that cannot be shared out is dead. If a run needs 1, 2 and 4 but two of its three cells can only be even, the combination fails however well it adds up. That step is the difference between the two easier difficulty bands.

The route shows the full table of forced combinations in Help, and will tell you which digits can still go in the selected cell. That is the same arithmetic done for you — a good way to learn the table rather than a substitute for it.

Every board has exactly one answer

That is not a claim about care taken; it is the gate every board passes through. A puzzle is built by filling a grid legally and reading the totals off it, which guarantees at least one answer. It is then handed to the solver and asked for a second one. If the solver finds another, the board is thrown away and a different one is made.

A board the solver could not finish checking within its budget is also thrown away. An unverified puzzle is refused rather than shipped — the safe direction is the only one available when the answer is “I do not know”.

What the difficulty bands mean

Each band names the weakest set of deductions that finishes the puzzle, so it is a promise about the solving rather than about the size.

• Gentle. Finishable by asking of each run what its length and total allow, and taking the cells where only one digit survives.
• Steady. Needs the next step: a combination is dead if it cannot be shared out among that run’s particular cells, given what each of them can still be.
• Tricky. Needs a longer chain than either — following a possibility several cells before it contradicts itself.

A puzzle you chose the difficulty of keeps no record, because a difficulty you picked is not comparable with one you were dealt.

Boards

Quick 7×7

The smallest board, and the one to start on. Short runs, few crossings, and every puzzle solvable by working out what a run can hold and nothing cleverer.

Standard 9×9

More cells and more crossings, so a run's own arithmetic stops being enough and you start needing what the crossing runs allow.

Large 13×13

A long sitting. Deliberately shorter runs than the smaller boards — with this many cells, longer ones stop being pinned down by their clues at all.

Daily puzzle

One Standard board, the same for everybody today, seeded from the date. Your time and hints are kept locally and nowhere else.

Choose a difficulty

Pick the board and the band. The band names the weakest set of deductions that finishes the puzzle, so it is a promise about the solving rather than about the size.

Privacy and local play

Your puzzle, your settings and your best times are stored on this device and nowhere else. There is no account, no sign-in and no gameplay request to any server.

The answer is not stored at all. What is saved is the puzzle’s seed — so the board is rebuilt each time — and an eight-character hash of the solution, which is enough to confirm a restored board is the one that was saved and gives nothing away. The reset button clears this game’s data and leaves every other Zerdly tool alone.

Questions

Does every puzzle really have only one answer?

Yes, and it is checked rather than hoped for. Every board is built by filling a grid legally and reading the clue sums off it, which guarantees at least one answer; it is then handed to the solver, which is asked for a SECOND answer. If it finds one the board is thrown away and another is made. A board the solver could not finish checking is also thrown away — an unverified puzzle is refused, not shipped.

What do the difficulty bands actually mean?

Each names the weakest set of deductions that finishes the puzzle. Gentle: asking of each run what its length and total allow, and taking the cells where one digit survives. Steady: that plus noticing a combination is dead because it cannot be shared out among that run's particular cells. Tricky: needing a longer chain than either. It is a promise about the solving, not about the size — a big board of short runs is gentler than a small one with two long runs crossing.

Why is the biggest board sparser than the small ones?

Because clue sums stop pinning a board down as it grows. Every white cell sits in exactly two runs, so runs of average length L give you two clues for every L cells — at length two that is one equation per cell, and by length four it is half. A 13×13 with long runs has so much freedom that most fillings have several answers, and the generator would refuse nearly all of them. Shorter runs are what make a big board a puzzle rather than a guessing game.

Do pencil marks count towards finishing?

Never. Nothing that judges the board — the completion check, the conflict marker, the hint — looks at them at all, and a cell's marks disappear the moment you write a real digit in it. They also sound different from a digit, so the two are never confusable.

What is the difference between Check and Hint?

Check tells you whether anything on the board is already wrong, and how many things, without saying which — it is the question 'am I still on track'. Hint gives you one specific cell and the reason it must be that digit. If something already on the board is wrong, the hint points at that instead, because a hint reasoned from a mistake is worse than no hint at all.

Does the hint ever guess?

No. It only offers a cell that follows from what is on the board by the same deductions a player could make, and it says which run forced it. When nothing follows in a single step, it says so rather than showing a digit it could not justify.

Can I read the answer out of my browser storage?

No. The board is not stored at all — only which puzzle it was, so it is rebuilt each time — and what is stored beside it is an eight-character hash of the solution rather than the solution. The list of puzzles the page downloads carries no answers either, for the same reason. The hash is there so a restored board can be confirmed to be the board that was saved. It is not a security measure and is not offered as one; anybody who wants to solve the puzzle themselves can have the answer.

Why did my saved puzzle disappear?

Because the puzzles changed. Your board is rebuilt rather than stored, so a different set would silently hand you somebody else’s answers on a board you had never seen. The version of the puzzle set travels with the save and a mismatch is refused rather than adapted, and the solution hash catches anything the version missed.

What is the Daily?

One Standard board, chosen by today’s UTC date, the same for everybody on the same version. Your time and hint count are kept on this device and nowhere else, along with a streak. The key includes the version, so a result stays attached to the puzzle it was earned on.

Is anything sent to a server?

No. The puzzles are made ahead of time and downloaded once as a small file, the way the site’s search index is; everything after that — the solver, the hints, the checking, the sounds and your saved puzzle — runs in your browser. If that file cannot be fetched the page makes a puzzle for you instead, which is slower but needs no server either. There is no account, and clearing this game’s data leaves every other Zerdly tool untouched.

More Zerdly Interactive

• Codebreaker — Deduction with feedback instead of sums, and a hint that cannot cheat.
• Sudoku — The other grid where a digit may not repeat in its line.
• Nonogram — Numbers down the side again, but they describe runs rather than sums.
• Zerdly Maths — Where the arithmetic under all of this gets its own practice.