How to Solve Nonograms (Picross): Rules and Strategies

What the numbers mean

A clue of 3 1 on a row means: somewhere in this row there is a run of three shaded cells, then at least one empty cell, then a single shaded cell, in that order from left to right. A clue of 0 means the whole line is empty. When every line matches its clue, the shaded cells form a picture.

Nonograms are also sold as Picross, Griddlers, Hanjie and Paint by Numbers. They were first published in Japan in 1987.

The overlap method

The single most useful technique: imagine the run pushed as far left as it can go, then as far right as it can go. Any cells covered in both positions must be shaded.

The rule of thumb: if a run of length k sits in a line of length n, and k is more than half of n, then 2k − n cells in the middle are certain. With several runs, add them up with one gap between each, and apply the same push-left, push-right idea to every run.

Edges and finished lines

Once a shaded cell touches an edge, the run it belongs to must start there. If the first clue in a row is 4 and the first cell is shaded, the first four cells are shaded and the fifth is empty.

When a line already matches its clue, mark every remaining cell as empty with an × (in our game, switch to Cross or right-click). Those crosses are information for the crossing lines.

Gaps, splitting and counting

Crossed-out cells split a line into segments. A segment that is shorter than the smallest run still to be placed can never hold a run, so cross it out too. When a line has two runs and a shaded cell sits between their possible ranges, ask which run it can belong to; often only one fits, which fixes that run’s position.

Counting helps on big grids. The total of a line’s clues plus one gap between each run gives the minimum space the line needs. If a row of 15 cells has the clue 4 5 3, the runs need 4 + 5 + 3 + 2 = 14 cells, leaving only one cell of slack. Push every run left, then right: almost every cell is decided at once.

A worked example: a 5×5 heart

Our smallest nonogram is a heart. The row clues from top to bottom are 1 1, 5, 5, 3, 1, and the column clues from left to right are 2, 4, 4, 4, 2.

1. Rows 2 and 3 have a clue of 5 in a line of 5, so every cell in both rows is shaded.
2. Columns 2, 3 and 4 have a clue of 4. Each already has rows 2 and 3 shaded; the overlap method shades rows 2–4 of each of these columns.
3. Row 4 now has its three middle cells shaded, matching the clue 3, so its first and last cells are crossed out.
4. Columns 1 and 5 have a clue of 2 and already contain rows 2 and 3, so rows 1, 4 and 5 of those columns are empty.
5. Row 1 needs 1 1 with its outer cells empty: the only arrangement left is columns 2 and 4. Row 5’s single cell must be in column 3, the only column whose run of 4 can still reach that far.

Five lines of reasoning and the heart appears, without a single guess.

Mistakes to avoid

• Shading from a hunch. Only shade a cell when every possible arrangement of the line shades it.
• Ignoring crosses. Empty cells carry as much information as shaded ones. Mark them.
• Reading clues out of order. Runs appear in the order given: a clue of 1 3 means the single cell comes before the run of three.

A routine for every puzzle

1. Start with the biggest clues: the lines where the runs nearly fill the line. Apply the overlap method.
2. Switch to the crossing direction. Every new shaded cell or × gives you a fresh constraint.
3. Complete lines whose clue is satisfied by crossing out the rest.
4. Use edges and gaps: a gap of empty cells too small for any remaining run must be crossed out.
5. Repeat until the picture appears. Every nonogram on our site is checked by a line solver, so this routine always finishes it without guessing.

Practice: play a nonogram.