How to solve nonograms

A nonogram looks like it needs a lucky guess to get going. It does not. Every puzzle on this site can be solved from start to finish by looking at one line at a time and asking two questions: which cells are shaded however the groups lie, and which are blank however they lie?

This page is the handful of ways to answer those two questions. With them you can solve any puzzle here without guessing once.

In the drawings, red is what the step works out: red hatching for a cell that must be shaded, a red cross for one that must be blank.

Start with the big numbers

Take a row of ten with the clue 7. Slide the group of seven as far left as it goes, then as far right. Whatever cells it covers both times are shaded, wherever it really lies.

A 7 in a row of ten: pushed left it covers cells 1–7, pushed right cells 4–10. Cells 4 to 7 are shaded either way.

A quick way to count it: take the number away from the length of the line, and that many cells at each end stay open. Ten minus seven is three, so three open at each end and the middle four shaded. Any number bigger than half the line shades something.

The same works with several groups. Push them all left, then all right, and look at each group on its own: where a group overlaps itself, those cells are shaded.

4 3 in a row of ten. Packed left, the 4 is on cells 1–4; packed right, on 3–6: cells 3 and 4 are shaded. The 3 is on 6–8 or 8–10, so cell 8 is shaded too.

Add the line up

Add the numbers of a clue together, plus one for every gap between groups. If that comes to the length of the line, the line is decided outright.

4 + 1 + 3, plus two gaps, is ten: the whole row. There is only one way to lay it.

The same goes for a 0, which is a whole line of crosses, and for a clue equal to the length of the line, which is a whole line shaded. Do these first: they are free.

Cross out as you go

It is tempting to mark only the shaded cells. Do not. A cross is as much information as a shaded cell, and most of the later steps start from one. Every time a line is finished, cross out whatever is left in it, so that the lines crossing it know.

The struck-through clue on the sheet tells you a line already makes its groups. Its remaining cells can all be crossed out.

The 2 and the 1 are both on the sheet, so the rest of the row is blank.

Work from the walls

The edge of the grid, and any crossed-out cell, is a wall a group cannot pass. A shaded cell against a wall is the start of a group, and you know its length from the clue.

A shaded cell against the edge, with the clue 3: the group must be those three cells, and nothing else in the row.

A shaded cell anywhere also limits how far its group can reach. If the only group is a 3 and cell five is shaded, the group lies somewhere within cells three to seven, and everything further away is blank.

A 3 that has to cover the shaded cell cannot reach the cells more than two away from it.

Gaps too small for any group

Between two walls, count the room. A gap shorter than every group that could go there is blank.

A 3 does not fit in the two cells before the cross, or in the one between the crosses: all blank. In the five cells left, the overlap shades the middle one.

This is where crosses pay for themselves. Late in a puzzle most of the progress comes from little gaps like these, and you only see them if the blanks are marked.

Join what must be one group

Two shaded cells that must belong to the same group are one group, so everything between them is shaded. If the clue is a single number, that is always the case. With several numbers, check whether any other group could fit between them.

Only one group, so the two shaded cells are part of it: the cell between them is shaded, and the 5 cannot reach the far ends.

The opposite also happens. A row with the clue 1 1 and two shaded cells side by side is impossible, so if you find that on your sheet, one of them is a mistake.

Rows against columns

None of these steps finishes a puzzle on its own. What finishes it is going round and round: every cell you decide in a row is a new fact for the column it sits in, and the other way about.

A good rhythm:

Do every full line, 0 and big number first.
Go through the rows once, applying everything above.
Go through the columns once.
Repeat, but only for the lines that changed since you last looked at them.

On a 20×20 the second and third pass usually find far more than the first, because the first pass has put walls and anchors everywhere.

When you are stuck

Every puzzle here can be solved line by line, so being stuck means there is a line you have not looked at hard enough. Look for:

a line whose clue is almost as long as the line after the crosses in it;
a shaded cell near a wall or a cross;
a gap between crosses smaller than the smallest group;
a clue whose numbers are all accounted for, but whose other cells are not crossed out yet.

And check the struck-through clues. A line can make its groups with the groups in the wrong places, and a wrong shaded cell will block you somewhere else later. Undo goes back as many strokes as you need.

Racing a friend

In a race, speed matters more than neatness, but a mistake costs far more than a few seconds: you will not find it until something does not fit.

Drag, do not click. A whole group is one stroke.
Clear the free lines first: zeros, full lines, sums that add up to the length.
Cross out only where it helps the next step; you do not need to cross out every blank cell to win.
Watch your friend's progress, not your own time. Lines done is a rough guide to who is ahead.

Ready? Solve a nonogram, or look up the rules again. If you like working things out from numbers, minesweeper is the other puzzle on the site.