How to solve a nonogram, step by step

You solve a nonogram one line at a time. Pick a row or column, work out what its clue allows, mark what’s certain, and move on. A handful of techniques do almost all the work. This guide goes through them one by one, then solves a small puzzle from start to finish.

Read the clues

Each number is a run of filled cells with no gaps in it. Row clues read left to right and column clues top to bottom, and the runs appear in that order. Between two runs there’s at least one empty cell, sometimes more. A clue of 0 means the whole line is empty.

One quick sum is worth learning early. Add up the numbers, then add one for each gap between them. For 3 1 2 that’s 3 + 1 + 2 + 2 = 8. If the total equals the length of the line, the clue fits only one way and you can fill the whole line at once. A 5 in a row of 5 works like this, and so does 1 1 1.

Fill the overlap

Big numbers are the place to start, because they have the least room to move. Push the runs as far left as they go, then as far right. Any cell a run covers in both positions is filled, whatever happens later. Compare each run only with itself: the 3 pushed left with the 3 pushed right, never with the 4.

There’s a shortcut. Take the length of the line and subtract the total from the quick sum: that’s the spare room. Any run longer than the spare room gets cells filled, as many as its length minus the spare room. For 3 4 in a row of 10, the total is 8 and the spare room is 2, so the 3 gets one cell and the 4 gets two. For a single 7 in a row of 10 the spare room is 3, so four cells fill.

Work from the edges

The edge of the grid stops a run, and so does a crossed-out cell. If a filled cell touches the edge, it’s the start of the first run (or the end of the last one). Fill the rest of that run and cross out the cell after it.

A filled cell close to the edge helps almost as much. The run has to include it, so it can’t start far from the wall.

Cross out empty cells

Crosses are half the solve. A cross in a row is a wall for the column it sits in, and that’s often what moves the puzzle on. Mark a cell as empty when:

• the line already has all its runs,
• it sits in a gap too short for any run that could go there,
• or no run can reach it.

Join and split runs

In a line with a single number, every filled cell belongs to the same run. If two filled cells have a gap between them, fill the gap. Then check how far the run can stretch from there: anything beyond that is empty.

With more numbers it can go the other way. Two filled cells too far apart for one run must belong to different runs. In a 2 2 line with the second and eighth cells filled, the second cell can only be in the first 2, because the second 2 needs room for the first one before it. The eighth cell is in the second 2. Neither run can reach the middle cells or the last one, so you cross those out.

Spot a finished line

A line is done when every number in its clue has a run of exactly that length, in the right order. Check each run against the clue, then cross out every unmarked cell left in the line. It’s tempting to skip this when it looks obvious, but those crosses are what the crossing lines need next.

A run is finished when both its ends touch a cross or the edge. If you find three filled cells together and 3 is the biggest number in the clue, that run can’t grow. Cross out the cell at each end.

Switch between rows and columns

One line rarely finishes on its own. Every mark you make in a row is new information for the column it sits in. So work in passes: go through the rows, then the columns, then the rows again. Whenever a line changes, look at the lines that cross it.

Every nonogram on Owlpuzzles can be finished this way without guessing. If you’re stuck, there’s always at least one line you can still make progress on.

Solving a 5×5 puzzle

Here’s a 5×5 puzzle solved with nothing but the techniques above. Rows count from the top, columns from the left. In each picture, the new marks are highlighted.

First pass on the rows

Row 1 is 0, so cross out all five cells. Rows 2 and 4 say 4. The spare room is 1, so the overlap fills their middle three cells. Row 3 says 1 2. The quick sum is 1 + 1 + 2 = 4, so the spare room is 1 again. The 2 covers the fourth cell wherever it goes, so fill that one.

Then the columns

Column 1 says 3. The top cell is crossed out, so the run has four cells to fit in, and it always covers the middle two of them: rows 3 and 4.

Columns 2 and 3 say 1 2. Below the cross there are exactly four cells, and 1 + 1 + 2 = 4 fits only one way: filled, empty, filled, filled. That fills row 5 and crosses out row 3 in both columns.

Column 4 says 3, and rows 2, 3 and 4 are already filled. That run is done, so cross out row 5.

Back to the rows

Row 3 (1 2) has its first cell filled and the next two crossed out. The first cell is the 1. The 2 has to cover the filled fourth cell, and it can’t use the crossed-out third, so it takes the fourth and fifth. Fill the fifth.

Row 4 (4) now has its first cell filled, right against the edge. The run is the first four cells, so cross out the fifth.

Row 5 (2) has its second and third cells filled. That’s the whole 2, so cross out the first and last cells.

The last few cells

Column 1 (3) has rows 3 and 4 filled and row 5 crossed out. The run can only go up, so fill row 2. Row 2 (4) now has its first four cells, so cross out the fifth. Column 5 already has its single cell in row 3. Every cell is marked, and the picture is a cup with a handle.

Questions about solving nonograms

Is there a trick to nonograms?

The nearest thing to a trick is the overlap: start with the biggest numbers, because they leave the least room. After that, crosses do most of the work, since each one is a wall for the line going the other way.

How do you solve a 15x15 nonogram?

The same way as a small one, with more lines to keep track of. Start with the lines that have the least spare room, then work the edges and crosses, and keep switching between rows and columns. Owlpuzzles grids go up to 20×20; on a phone, pinch to zoom in and the clues stay in view.

What should I do when I’m stuck?

Go through every line once more and ask what its clue rules out, not only what it fills. Look for gaps too short for any run, and for runs at full length that don’t have crosses at both ends yet. Then try the daily nonogram again.