Do the numbers in a nonogram have to be in order?

Yes. The numbers are listed in the order the runs appear along the line, left to right for a row and top to bottom for a column. That ordering is half the information they carry.

Is a nonogram a maths puzzle?

No more than sudoku is. The numbers are lengths, not quantities to add up, and the only arithmetic that ever helps is counting slack. It is a constraint puzzle that happens to be written in digits.

How long should a 15 × 15 nonogram take?

Ten to twenty-five minutes once the overlap sweep is second nature; considerably longer the first few times, because most of the clock goes on lines you have not yet learned to skip.

What happens if I paint a square by mistake?

Nothing breaks — tap it again to clear it, or press Undo. Wrong squares are not rejected, because a nonogram that refused illegal marks would be solving itself; the board only tells you when a whole line has become impossible.

How to Play Nonograms

Nonograms give you a grid with numbers beside every row and above every column. Those numbers are the lengths of the painted runs in that line, in order, with at least one blank between them. Work out which squares must be painted and which must be blank, using rows and columns against each other, and the painted squares form a picture. A correct nonogram never needs a guess.

The rules, step by step

1Read the numbers as run lengthsEach number beside a row or above a column is the length of one painted run, and the numbers are in the order the runs appear along that line.
2Leave a gap between runsTwo consecutive numbers mean two separate runs, so there is at least one blank square between them. That gap is part of the room they need.
3Paint only what is forcedA square is painted when every arrangement of its line's numbers that still fits the marks would paint it. Anything less than that is a guess.
4Cross out what cannot be paintedA square no surviving arrangement would paint is blank, and marking it as blank is what lets the next deduction in that line and the crossing one happen.
5Use rows and columns against each otherA square settled by a row constrains the column through it, and the other way round. Sweeping both directions in turn is the whole method.
6Finish the picture to winThe puzzle is solved when exactly the picture's squares are painted. Crosses are your own bookkeeping and are never checked, so an uncrossed grid still wins.

Try it — the rules above, running

Time0:00Painted0 / 53Size10 × 10Puzzle#20260918

New puzzle draws a fresh picture at the size you last chose, Hint makes one deduction and says which line it came from — and points out a wrong mark first, if there is one. The three-dot menu holds the auto-crossing switch, check-as-you-go, today’s shared puzzle and the size.

Your statistics · 10 × 10

Played: 0
Won: 0
Win rate: 0%
Streak: 0
Best streak: 0
Best time: —

This size

100 cells, twenty lines. Long runs overlap themselves at the first pass, and from there it is crossing out that keeps the deductions coming.

Keyboard and mouse

Arrows: Move the cursor
Enter: Paint or clear that square
X: Cross out or clear that square
Right click: The other mark, leaving the tool alone
U: Undo
F: Full screen

Where do you start a nonogram?

1Find the full linesA line whose numbers plus gaps exactly fill it has no freedom at all: paint it straight in. A line marked 0 is the same deduction in reverse — cross the whole thing out.
2Sweep for overlapsFor every line with a run longer than half its length, push the run left, push it right, and paint the squares covered both times. That is 2b − n squares for a single run of b in a line of n.
3Turn ninety degreesNow do the same for the columns. The squares the rows just settled are constraints the columns did not have a moment ago, so lines that gave nothing the first time will give something now.
4Cross out everything you canAny square that no arrangement of its line would paint is blank. Mark it. Each cross shortens the space the runs in the crossing line have to live in.
5Repeat until the picture appearsKeep alternating. The hardest 15 × 15 in this library keeps paying out for eight sweeps of its thirty lines; 22 of the 34 puzzles at 10 × 10 give up everything in one sweep or two.

What does crossing out actually buy you?

It converts a blank square into a wall. A run cannot cross a cross, so a single cross can split a line into two shorter segments, and a segment shorter than the run that would have to sit in it rules that run out entirely. That is how a line with no overlap at all suddenly resolves.

The effect is measurable. Take the solver used to vet these puzzles, and forbid it from ever recording a blank square: 82 of the 91 puzzles here stop before they are finished, including all 34 at 10 × 10 and all 25 at 15 × 15. Only nine of the 5 × 5s survive the handicap. A player who never crosses is playing a harder game than the one that was designed.

What techniques come after the overlap?

Edge forcing — if the first square of a line is painted, the first run starts there, so the rest of it is determined and the square after it is blank.
Segment elimination — a stretch of open squares shorter than the smallest run still to be placed can be crossed out entirely.
Run completion — a painted block already as long as the run it belongs to is finished, so cross the square at each end.
Counting from a wall — from a cross, count the first run's length: squares beyond the reach of every remaining run are blank.
Simple boxes after marks — redo the overlap on what is left of a line once its crosses have shortened it. It very often forces something the first pass could not.

How do you recover from a mistake in a nonogram?

Stop as soon as a line's numbers turn red. A contradiction means no arrangement of that line's numbers fits its marks, so at least one mark in it is wrong — but the wrong mark is often in a crossing line, put there several deductions ago. Undo back to the last position you are sure of rather than trying to patch it; the marks that followed a wrong one are all built on it.

The hint button is built for exactly this. It checks the grid against the picture before it does anything else, and if it finds a square painted where the picture is blank, or crossed where the picture paints, it says so and fixes that square first. Only on a clean grid does it make a fresh deduction, and then it names the line and how many arrangements it argued from.

How do you win more often?

Open with the overlap sweep on every lineFor a single run of b in a line of n, 2b − n squares are forced before anything else is known — three squares from a 4 in a five-wide row, nine from a 12 in a fifteen-wide one. Do every row, then every column, before attempting anything cleverer.
Cross out as hard as you paintEvery 10 × 10 and 15 × 15 puzzle here provably stalls for a solver that never records a blank square. A cross is not a note to yourself; it is the fact that unlocks the run next to it, so place them as soon as they are certain.
Work the line with the least slackAdd the numbers, add one gap between each pair, subtract from the line length: what is left is all the freedom that line has. A line with slack of one or two is nearly determined and will usually give up more squares than a line you merely find interesting.
Grow from a painted square, not from an empty lineOnce one square of a run is painted, count outward: if the run is five long and the square is two from a cross, the far end is pinned and everything beyond it can be crossed. Extending known blocks is faster than restarting a line from its numbers.
Use a finished line as a wallWhen a line's painted runs already match its numbers it is done, and every remaining square in it is blank. This board crosses those for you, and the crosses immediately shorten every crossing line — which is exactly where the next deduction comes from.
Treat a contradiction as a stop signIf a line's numbers can no longer be fitted around its marks, the board turns that line's numbers red. Do not push on: something earlier in that line or in a line crossing it is wrong, and every square you add on top of it is built on sand.

Common questions about nonogram

Do the numbers in a nonogram have to be in order?: Yes. The numbers are listed in the order the runs appear along the line, left to right for a row and top to bottom for a column. That ordering is half the information they carry.
Is a nonogram a maths puzzle?: No more than sudoku is. The numbers are lengths, not quantities to add up, and the only arithmetic that ever helps is counting slack. It is a constraint puzzle that happens to be written in digits.
How long should a 15 × 15 nonogram take?: Ten to twenty-five minutes once the overlap sweep is second nature; considerably longer the first few times, because most of the clock goes on lines you have not yet learned to skip.
What happens if I paint a square by mistake?: Nothing breaks — tap it again to clear it, or press Undo. Wrong squares are not rejected, because a nonogram that refused illegal marks would be solving itself; the board only tells you when a whole line has become impossible.

Ready to stop reading? Play nonogram on the full board, with controls and statistics tailored to that game.