Nonogram techniques: how to solve nonograms step by step

Technique 1 · basic

Full lines and zeros

Start every puzzle by adding up each clue: the numbers, plus one gap between each pair of them. If the total equals the width of the board, the runs fit in only one place, and the line is decided from end to end. On a 7x7 board, 4 2 is 4 + 1 + 2 = 7, and 2 2 1 is 2 + 2 + 1 plus two gaps, also 7. Fill the runs and cross out the gaps at once. The crosses matter as much as the boxes: each one is a wall for the line that crosses it, and walls are what the next techniques push against.

A clue of 0 is the other free gift: the whole line stays empty, so cross it all out before anything else. Rowcall gives every line at least one number, but nonogram books use 0 often. Also note the lines that come close to the full width: one or two tiles of slack feed the overlap straight away.

Where to look: clues with many numbers or one big number. Add them up before you touch a tile.

Technique 2 · basic

Overlap (simple boxes)

Push all the runs of a line as far left as they go, then as far right. A tile that the same run covers in both positions is a box, wherever that run really sits. The quick way to count: the slack is the width minus the full length of the clue, numbers plus gaps. Each run longer than the slack gives its length minus the slack in boxes, from its middle. On a 7-wide row, 3 2 needs six tiles, so the slack is 1: the 3 gives two boxes and the 2 gives one. A single 5 on seven tiles has a slack of 2 and gives three boxes.

Compare each run only with itself. The 3 pushed right and the 2 pushed left may cover the same tile, but a tile covered by two different runs proves nothing. Run the overlap on every line of a new board: it opens almost every nonogram, and it works again later on the shorter stretches between crosses.

Where to look: big numbers, and clues whose total comes within two or three tiles of the width.

Technique 3 · basic

Simple spaces

Crosses cut a line into stretches of open tiles. A stretch shorter than the smallest number in the clue can't hold any run, so every tile in it stays empty. Look between two crosses, and between a cross and the edge of the board: two open tiles in a line whose clue is 3 are dead. The same goes for tiles that no run can reach, such as tiles beyond the furthest position of the last run. Crossing them out is not busywork: each new cross is a wall for the row or column that runs through it.

Once the dead stretches are gone, count again what is left. Here the 3 has only one stretch that can hold it, three open tiles long, so it fills that stretch exactly: a full line inside a line. Simple spaces and the overlap often take turns like this. One removes room, the other uses the room that is left.

Where to look: lines with a cross near the edge, and short gaps between two crosses.

Technique 4 · intermediate

Glue: boxes near the edge

A box near the edge of the board, or near a cross, is glued to it. If the open tiles in front of the box are fewer than the first number of the clue, the first run can't fit there, so the box belongs to that run. The run then has to reach at least its own length out from the wall, and every tile from the box up to that point is a box. A box right on the edge with a first number of 3 fills that tile and the next two. Use it from both ends: the last run is glued to the far wall in the same way.

Glue gives the most when the box sits right against the wall, and that box often comes from a full line or an overlap in the other direction. Once the run has its full length, close it with a cross, as the next technique shows.

Where to look: boxes in the first or last two or three tiles of a line, and boxes just past a cross.

Technique 5 · intermediate

Closing a complete run

When a run of boxes is as long as the biggest number in the clue, that run is complete: it can't grow, because no number in the clue is longer. Cross out the tile on each side of it. Some solvers call this punctuating. It works for smaller numbers too once you know which run is which, for example the first run glued to an edge. The two crosses are quick to find and often unlock the crossing lines, because each one is a new wall for the line it sits in.

Be careful with runs shorter than the biggest number. A run of 2 in a line with clue 2 3 might still be the start of the 3, so don't close it until the order of the runs or the space around it rules that out.

Where to look: runs of boxes that match the largest number in their clue, above all big numbers like 4 or 5.

Technique 6 · intermediate

Joining

Two boxes in one line, with open tiles between them, must be joined when they belong to the same run: the run covers both, so it covers every tile between them. A clue with a single number is the simple case, since every box in that line is part of the one run. With several numbers, first work out which run each box belongs to, usually from the edge, from a cross, or from runs you have already placed. Then check that the run is long enough to cover both boxes, and fill the gap.

In the example the first box sits on the edge of the row, so it is the 1, and the cross after it closes that run. The other two boxes can only belong to the 3, and a 3 that covers both of them has to fill the tile between them.

Where to look: boxes two or three tiles apart in a line with few numbers.

Technique 7 · intermediate

Splitting

Splitting is the opposite of joining. If filling the tile between two runs would make one run longer than the biggest number in the clue, that tile stays empty. Add the two runs and the tile between them; if the total is bigger than every number, cross the tile out and the runs stay apart. In lines with clues like 1 3 or 2 2 it comes up all the time, because a box and a pair of boxes one tile apart look as if they could become one run of four.

Splitting gives one cross, but a useful one: it tells you that the two runs are different numbers of the clue, and often which ones. Here the single box can only be the 1 and the pair belongs to the 3. The cross blocks the 3 on the left, so it can only grow to the right.

Where to look: two runs with a single open tile between them, in lines with small numbers.

Technique 8 · intermediate

Mercury

Mercury is a special case of simple spaces, named for the way mercury pulls back from the walls of its glass. It happens when a box sits exactly the first number's length away from the wall: the open tiles in front of it are just enough for the first run, but a run there would touch the box and merge with it. So the box belongs to the first run, and that run can't reach the wall. Cross out the tile against the wall. Check for it from both ends of the line.

It looks like a small gain, a single cross. But it turns up in lines where the overlap and glue give nothing, and that one cross is a new wall for the row or column it sits in. It also settles which run the box belongs to, and the next steps in that line build on that.

Where to look: a box with exactly the first number's worth of open tiles between it and the edge or a cross.

Technique 9 · intermediate

Crossing rows and columns

No line solves on its own for long. Every box or cross you add sits in one row and one column, so after each step, look at the line that crosses it. A row that gave nothing on an empty board can open up as soon as a column puts a box in it. Work in passes: rows, then columns, then rows again, and only revisit lines that gained a tile since you last looked at them. On hard boards this back and forth is the whole game, with each pass giving only a tile or two.

Keep a short list in your head. When a step adds tiles to a row, note the columns it touched and go to those next, starting with the one that gained the most. It saves scanning the whole board after every move.

Where to look: lines that just gained a box near their middle or a cross near one end.

Technique 10 · advanced

Line contradiction

When the quick techniques run dry, take one open tile and ask what would happen if it were filled, or empty, using only its own line. If one choice leaves no way to place the runs of the clue, the tile must be the other. This is not guessing: you test a single line, not the whole board, and the check ends within a few moves. Start with tiles next to a box and with short lines that already have a few tiles known, where the runs can sit in only a handful of ways.

Every Rowcall puzzle can be finished with line logic like this, so you never have to guess across the whole board. If no tile in any line leads to a contradiction, you have missed an easier step: go back to the overlap and simple spaces on the lines that changed last.

Where to look: the tile right next to a lone box, in a line whose last number is small.

Common mistakes

• Comparing two different runs in the overlap. A tile is a box only when the same run covers it in both the leftmost and the rightmost position. One run on the left and another on the right covering the same tile proves nothing.
• Forgetting the gaps when you add up a clue. 3 1 2 needs 3 + 1 + 2 tiles plus two gaps, 8 in all. Leave the gaps out and you see room that isn't there.
• Skipping the crosses. A cross is information, not decoration. Simple spaces, glue and mercury all push against crosses, so a tile you know is empty but haven't crossed out hides the next step. Turn on Auto crosses in settings if you tend to skip them.
• Closing a run too early. A run of boxes is complete only when no number in the clue is longer, or when you know which number it is. A 2 in a line with clue 2 3 may still be the start of the 3.