The Move That Needs Nothing

This reads the numbers and the length of the line and nothing else. Everything it has to say is available before a single cell has been marked.

Push everything left, push everything right, keep the overlap

Take one line and imagine its runs crammed as far towards the start as the rules allow: each number in turn, one blank between consecutive pairs, nothing wasted. Now imagine them crammed as far towards the finish. Any cell covered by the same run in both of those arrangements is covered by that run in every arrangement, because the run can only ever sit between those two extremes. So it can be filled.

The arithmetic is small enough to do in your head. Add the numbers, add one for each gap between them, and subtract from the length of the line: that is the slack. Any number bigger than the slack contributes cells, and the count it contributes is the number minus the slack. A twenty-cell row reading 6 4 has a slack of nine, so nothing overlaps; the same row reading 14 has a slack of six and hands over eight cells at once.

On an empty board this is the only argument available, which is why every nonogram opens the same way: find the biggest numbers, work out their slack, and fill the middles. It is also worth doing once and thoroughly rather than repeatedly, because on a blank line it never has anything further to say.

what it decides what it wrote

The two lines it settles outright

A line with no numbers is entirely blank, and every one of its cells can be crossed off immediately. These are the cheapest cells on any board and the ones beginners most often leave alone, because a nought does not look like information. It is the strongest clue on the board: every cross it produces is a wall in some other line.

A line whose slack is zero is completely determined. Write the runs in with their single gaps and the whole line is done in one movement, no reasoning required beyond the addition. On a small board there is usually one of these, and it is where to start.

Both are the same arithmetic as the overlap, taken to its extremes, which is why they share a rung. Nothing about either asks you to look at a cell.

What this rung will never do

It will never cross a cell out in a line that has numbers in it. Overlap proves that certain cells are filled; it says nothing about which are blank, because on a line nobody has touched every cell is reachable by some run. Crosses come from the rungs above, and from the walls that finished lines leave behind.

It also never improves. Because it reads only the numbers, running it again after twenty moves gives exactly what it gave at the start. That is unusual on this site — most rungs on most puzzles get sharper as the board fills — and it is the reason a nonogram solve has such a distinct opening phase, followed by a completely different middlegame.

Where this sits on the ladder

• Rung 1Overlap

  A run longer than half the line has to cover the middle of it, wherever it sits.

• Rung 2Working in from the ends

  What the settled cells at the two ends of a line force, without looking between them.

• Rung 3Gaps and splitting

  The crosses cut the line into pockets, and each number has to fit into one of them.

• Rung 4Glue

  A filled block you can see at a glance belongs to a run, and that says how far it reaches.

• Rung 5The whole line at once

  One or two filled cells adrift in an open stretch, read with everything else on the line.

• Rung 6Assumption

  Fill a cell on spec, follow it until a line breaks, and rub it out again.

Common questions

More Nonogram pages

• Nonogram puzzleUnlimited boards
• Daily nonogramA new picture every day
• Nonogram rulesOne rule, in full
• Solving a boardA 20×20, worked
• Nonogram techniquesThe whole ladder
• 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