Nonogram

How to play a nonogram

Every row and every column carries a clue: a list of numbers giving the lengths of the runs of filled cells in that line, in order, reading left to right for a row and top to bottom for a column. Between two consecutive runs there is at least one blank cell. Fill the cells that must be filled, cross out the ones that must be blank, and a picture appears.

Drag to paint a whole run at once — the stroke locks to the row or column you started along, so a wandering hand cannot fill the line below. Right-click, or hold Shift, or press X, to cross instead of fill. Undo is unlimited and one press undoes one drag, crosses included.

Two conveniences on this page that a paper solver does with a pencil and most free sites make you hold in your head: a clue number dims once its run is settled, and the crosshair runs from the cell you are hovering all the way out through its clues, so you never have to count rows to find out which clue you are reading.

The three things almost everyone gets wrong

1. The clue is a sequence, not a set

1 2 is not the same clue as 2 1. The first means one filled cell, then a gap, then a run of two, in that order along the line. A line that satisfies one does not satisfy the other, and reading a clue as an unordered bag of numbers is the single most common way to lose a puzzle you had otherwise solved.

2. A clue of 0 is a clue

It means the line is entirely blank and every cell in it can be crossed out immediately. It is free information and it is the fastest opening move on any board that has one. It is also the case that breaks naive solvers, which read 0 as "a run of length zero" and produce nonsense — which is why our engine treats an empty clue as its own case and our test suite asserts it in both directions. Four of the twelve published puzzles the suite runs against contain a genuinely blank line.

3. Crossing out is a deduction, not a decoration

A crossed cell is something you have proved, and it does as much work as a filled one: it is what closes a run so the next block can be pinned down. On this page a cross is a real state with its own mark, and undo restores it as one. Sites that treat "crossed" as merely "not filled" lose your reasoning every time you step back.

One solution, and no guessing — two different promises

A puzzle with two solutions is not a hard nonogram, it is a broken one. If a clue set can be completed two different ways, then at some point every remaining deduction is impossible and the only way forward is to pick a cell and see. That is the most commonly shipped defect in this genre, exactly as it is in sudoku, because checking for it costs a solver run per candidate picture and generators that skip the check are much faster to write.

But uniqueness is not enough, and this is the part worth the page. A puzzle can have exactly one solution and still be unreachable without guessing. That is not a theory: Jan Wolter's published paint-by-number test set — the one our engine is checked against — contains seven puzzles that are "definitely unique" and still require lookahead or a guess. A site that only checks uniqueness will happily serve you one of those and call it expert.

Our generator makes both guarantees at once, and it makes them by construction. It draws a picture, derives the clues, and keeps the picture only if a named line-by-line rule ladder can finish it from a blank grid with no branching anywhere. Because every rung of that ladder is a forced deduction, a puzzle the ladder finishes has exactly one solution for free — and we test both anyway, with two solvers that share no code.

What we check against, and it is unusually good

The anchor for this engine is Jan Wolter's "Sample Paint-by-Number Puzzle Set", the test set behind his Survey of Paint-by-Number Puzzle Solvers. Twelve of its puzzles are named in his README as freely redistributable with attribution, and those twelve — and only those twelve — are in this repository, with their titles, authors and copyright lines intact.

What makes it a better anchor than a list of answers is that it publishes properties. Every puzzle in it carries Wolter's own verdict in the file: whether it is "definitely unique", and whether it is "definitely line/color solvable", "definitely requires moderate lookahead", or "may require some guessing". So our test suite checks four separate things against data we did not choose and cannot tune to:

• the clues we derive from each published picture are the published clues — all 12 puzzles, 732 lines;
• the solution our solver returns is the published picture — all 12;
• each has exactly one solution, matching "definitely unique" — all 12, confirmed by two independent solvers;
• and the one that means the most: our line solver finishes exactly the five he marks line-solvable and stalls on exactly the seven he does not — 12 out of 12.

That last check is a twelve-way classification match, not a single answer. A line solver that was too weak would fail the first five; one that was unsound would "solve" some of the other seven. Neither happens.

Difficulty here is a measurement, not a grid size

Nearly every free nonogram site grades by how big the grid is. We built a named technique ladder to grade by the hardest rule required instead — and then measured it over 2,400 random pictures at four sizes, and it barely discriminates: one rule, constrained block packing, decides over 96% of all solvable puzzles, and the full line intersection is required in well under 1%. Grading by hardest rung would have been difficulty theatre.

So the number this page grades on is different: the tightest moment — the fewest lines anywhere on the board that can still be advanced at the hardest point of the solve. A puzzle where twelve lines are always ready is a pleasant scan; one where at some moment exactly one line out of forty will move is a hunt, and that is what difficulty actually feels like. It is a property of the puzzle, it is computed before you are dealt it, and it is printed beside the board.

The hint tells you the rule, not the answer

A hint that fills in a cell teaches you nothing, which is exactly why the sites that meter hints can get away with metering them. Ours names the rule and gives the argument — "push row 7's blocks (4 2) as far left as they go, then as far right; three cells are covered both times, so they are filled whichever way the line ends up" — highlights the line it applies to, and fills in nothing. It always offers the easiest rule available, because a hint that opens with a full line intersection while a settled line is sitting there is teaching the wrong lesson. It is unlimited and free.

Check reads the board, not the picture. It reports lines whose clue cannot be satisfied by what is currently written in them. It deliberately does not say "you are doing fine", because a board can be perfectly legal so far and still contain a cell the real picture does not have.

The honest limitations

Nonograms are NP-complete in general, and we have not fixed that. Deciding whether a nonogram has a solution at all is NP-complete — Nobuhisa Ueda and Tadaaki Nagao, "NP-completeness results for NONOGRAM via Parsimonious Reductions", Tokyo Institute of Technology, 1996. We cite it; we do not claim to have beaten it. What our engine does instead is sidestep it: it refuses to deal a puzzle whose solution needs search, and proves that property on the individual puzzle before it is drawn. That is a guarantee about our puzzles, not a general algorithm.

Our line solver has a hard limit and here is exactly where it is. On published puzzle #23, "Nonrepresentational Test Pattern" — Wolter's own demonstration of why grid edges matter — our line-by-line solver makes zero deductions. Not a few, zero, because from the opening position no single line can be advanced at all. Our test suite asserts that, so if someone later adds a rule that reads two lines at once, the test fails and this paragraph gets rewritten on purpose rather than rotting quietly. It does not affect the puzzles we deal you — they are generated inside what the line solver can do, so the hint always works on them.

The independent cross-check has a size limit, and we say which. Uniqueness on every puzzle we generate, at every size from 5×5 to 20×20, is proved by a second deliberately-stupid counting solver that shares no code with the one that made the puzzle. On the published set that oracle is exponential and refuses past a few hundred cells, so it verifies four of the twelve and the other eight rest on the fast solver alone. That is a limit of the check, not of the engine, and the suite prints which puzzles it refused rather than dropping them silently.

Strategy that actually helps

Start with the lines that fill themselves. A clue whose blocks plus their mandatory gaps add up to the width of the line is completely decided before you do anything — and so is a clue of 0. On a 15-wide grid, "5 4 3" is 12 cells of block plus 2 mandatory gaps, which is 14: one spare cell, and almost the whole line is forced.

Then overlap. Push a line's blocks as far left as they will go, then as far right. Any cell covered by the same block both times is filled no matter how the line resolves. This one rule opens most boards, and on a 20-wide line a single block of 12 gives you four guaranteed cells before you know anything else.

Cross out as aggressively as you fill. Beginners fill and leave the rest blank. Crossing is what closes a run so the next block can be pinned, and a cell you have proved empty is worth exactly as much as one you have proved full. Most of the second half of a hard nonogram is crosses doing the work.

Work the crossing line, not the next row down. When you fill a cell, the line that just got new information is the perpendicular one. Following the crossing line is the difference between solving and scanning.

Never guess, on this board. On most sites that advice is unenforceable. Here it is a property of the puzzle: if you cannot see the next step, one exists, and the hint will name it.

Questions people ask

How do you play a nonogram?

Each row and each column has a clue: a list of numbers giving the lengths of the runs of filled cells in that line, in order, reading left to right or top to bottom. There must be at least one blank cell between consecutive runs. Fill the cells that must be filled and cross out the ones that must be blank until the picture appears. A clue of 0 means the whole line is blank.

Does clue order matter in a nonogram?

Yes, and it is the rule beginners most often lose a puzzle to. A clue of 1 2 means a single filled cell, then at least one blank, then a run of two — in that order. It is not the same clue as 2 1, and a line that satisfies one does not satisfy the other. The numbers are a sequence, not a set.

Does every nonogram have exactly one solution?

A proper one does, and a puzzle with two solutions is not a hard nonogram — it is a broken one, because at some point every remaining deduction is impossible and the only way forward is to pick a cell and see. Plenty of free generators never check. Every puzzle on this page is proved to have exactly one solution before you see it, and our test suite re-proves it with a second, independently written counting solver that shares no code with the one that made the puzzle.

Do I ever have to guess in a nonogram?

Not here, and this is a stronger promise than uniqueness. A puzzle can have exactly one solution and still be impossible to reach without guessing — Jan Wolter's published test set contains seven puzzles that are "definitely unique" and still require lookahead. Every puzzle we deal is generated by keeping only pictures whose clue set can be finished one line at a time, so a pure-logic path exists by construction, not by hope.

What does a clue of 0 mean in a nonogram?

It means that line is entirely blank — every cell in it can be crossed out immediately. It is a real clue, not a missing one, and it is the case that breaks naive solvers, which read 0 as "a run of length zero" and produce nonsense. Four of the twelve published puzzles our test suite runs against contain a genuinely blank line, so it is not hypothetical.

Are nonograms hard for a computer to solve?

In general, yes: deciding whether a nonogram has a solution is NP-complete, proved by Nobuhisa Ueda and Tadaaki Nagao in 1996. We cite that rather than claiming to have improved on it. What our engine does instead is refuse to deal a puzzle that needs search at all — every puzzle here is solvable by a polynomial line-by-line method, and that property is proved on the individual puzzle before it is drawn.

Is it called nonogram, picross, hanjie or griddlers?

They are the same puzzle. The word on this page is nonogram, deliberately: Picross is a Nintendo trademark, and Griddlers and Hanjie are used commercially by other publishers. The puzzle itself is public domain. The split naming is also why no single site collects all of the demand — the same person may search "picross online", "hanjie", "japanese crossword" or "paint by numbers puzzle" and land somewhere different each time.

What makes one nonogram harder than another?

Not the grid size, which is what almost every free site grades by. We measured our own technique ladder over 2,400 random pictures and it barely discriminates — one rule, constrained block packing, decides over 96% of solvable puzzles. So difficulty here is a different number: the fewest lines anywhere on the board that can still be advanced at the hardest moment of the solve. On Gentle there are never fewer than five places to work; on Tough there is a point where one or two of the forty lines will move and you have to find them.

Is this nonogram game free?

Yes. No signup, no account, no daily puzzle limit, no ads between you and the grid, no paid hint packs, no mistake limit that ends a puzzle you were solving. Undo is unlimited, hints are unlimited. Nothing on this page is metered.

Where nonograms come from

The puzzle was arrived at twice, independently, in Japan. In 1987 the graphics editor Non Ishida won a Tokyo window-art competition with images made by switching the lights of a skyscraper on and off, and turned the idea into puzzles she published as Window Art Puzzles. At about the same time the professional puzzler Tetsuya Nishio invented the same thing and published it in another magazine. James Dalgety in the UK coined the English name nonogram, after Ishida, and The Sunday Telegraph began running them weekly in 1990.

The puzzle type is public domain — two independent inventors, no publisher's claim on the idea. Several names for it are not: Picross is a Nintendo trademark, and Griddlers, Pic-a-Pix and Hanjie are used commercially by other publishers, which is why this page says nonogram everywhere. No publisher's puzzle set, styling or interface has been copied here; every puzzle you are dealt was generated by the code in play/nonogram-engine.js. The twelve published puzzles our test suite checks against are used under the attribution licence their author granted, and are named with their authors in data/nonogram-webpbn.json.

The honest small print

Your completed puzzles and times are stored as unverified, because a browser can lie about its own score and we would rather label it than pretend otherwise. Pictures are seeded, so the same seed always gives the same picture — the seed is shown beside the board. "Give up" reveals the picture and is deliberately a separate button that says what it does; nothing on this page ever fills a cell for you unless you ask it to. The pictures are procedurally generated rather than drawn by a person, so they read as abstract shapes rather than as recognisable objects — that is a real difference from a hand-authored puzzle set and we would rather say it than let you discover it. Finishing is judged on the clues, not on matching the stored picture, so you never have to cross a single cell to be counted as solved.