The Rules of Nonograms

There is only one rule here, which makes this the shortest rules page on the site and the one where the small print does all the work.

The numbers are run lengths, in the order they occur

Take any line — a row or a column — and read the numbers beside it from left to right, or from top to bottom. Those are the lengths of the filled stretches in that line, listed in the order you meet them travelling along it. A line labelled 2 5 1 contains a stretch of two, then later a stretch of five, then later a stretch of one, and nothing else is filled anywhere in it.

Order is part of the statement and it is the half people drop. 2 5 1 and 1 5 2 are different clues, and a line satisfying one of them almost never satisfies the other. When you check a line you have finished, read it in the same direction as the numbers rather than glancing at it and counting what you see.

Nothing in the rule says where any of the runs are. That is the puzzle, and it is why a nonogram is solved a line at a time by working out what all the possible placements agree about rather than by placing anything.

Between one run and the next there is always a gap

Consecutive runs are separated by at least one blank cell — otherwise they would be a single longer run and the numbers would say so. This is what makes the arithmetic in the puzzle work: a line labelled 3 3 needs a minimum of seven cells, not six, because the seventh is the gap that keeps the two threes apart.

Add the numbers, add one for each gap between them, and you have the shortest the line could possibly be. Compare that with how long the line actually is and the difference is the slack — the only quantity in this puzzle worth calculating before you start. A line with no slack is completely determined before you have read a single cell.

Nothing constrains the blanks at the two ends. A line may begin filled, end filled, both or neither, and the leading and trailing gaps may be any length including nothing at all. Only the gaps between runs are compulsory.

A line marked nought, and a line with no slack

A line with no numbers at all is entirely blank. It is drawn here as a nought, and it is the single most useful thing that can appear on a board: every cell in it can be crossed off before you have looked at anything else, and each of those crosses is a wall in some other line.

At the opposite end sits a line whose numbers plus their compulsory gaps come to exactly its length. It has one possible arrangement and can be written in immediately. On a fifteen-cell row that means something like 4 3 5, and on a small board these are where you begin.

Everything between those two extremes is the actual puzzle, and how much room a line has is exactly how little it will tell you on its own. That is why nonograms are not solved line by line in isolation — a row hands you two cells, those two cells are in columns, and the columns hand you back four more.

Four things people take the rules to mean

They do not say the picture is symmetrical, connected, or a recognisable object. Nothing about the drawing is a clue and nothing about it may be assumed — guessing that a shape is probably a heart and filling in the rest is not solving, and on the generated practice boards there is no shape at all.

They do not say a number tells you which run of the picture it is. A 4 in a row is a run of four somewhere in that row; it is not the fourth of anything and it is not connected to the 4 in the row below.

They do not say a filled cell has to touch another one. Runs of one are common and are the hardest thing on the board, because a single cell is the piece of information that constrains a line least.

And they do not permit guessing. Every board published here was checked to be finishable by argument alone, so a board that will not move is one where something has been missed rather than one that wants a coin flipped. That is a promise about the library and the generator, and it is why so much of the generator’s work gets thrown away.

Common questions

More Nonogram pages

• Nonogram puzzleUnlimited boards
• Daily nonogramA new picture every day
• Solving a boardA 20×20, worked
• Nonogram techniquesThe whole ladder
• OverlapTechnique — the opening
• The ends of a lineTechnique — easy
• Gaps and splittingTechnique — medium
• GlueTechnique — hard
• The whole lineTechnique — expert
• Guessing at nonogramsTechnique — refused
• Printable nonogramsFor paper
• Nonogram archiveEvery past picture