Nonograms (Picross, Griddlers): how to solve picture logic puzzles

Updated 2026-10-30

A nonogram is a grid puzzle where number clues beside each row and column tell you which cells to fill in; solve it correctly and a hidden picture appears. The puzzles go by many names, including Picross, Griddlers, Hanjie and Paint by Numbers, but the rules are the same.

Nonogram rules

You start with an empty rectangular grid. To the left of each row, and above each column, is a list of numbers. Each number is the length of a run (or block) of consecutive filled cells in that line. The rules are:

• The runs appear in the same order as the numbers, left to right for rows and top to bottom for columns.
• Between two runs there must be at least one empty cell.
• There may be any number of empty cells before the first run, between runs, and after the last run.
• A clue of 0 (or no clue) means the line is completely empty.

So a row with the clue 3 1 contains a block of three filled cells, then at least one gap, then a single filled cell. Every cell ends up either filled or empty, and a good nonogram has exactly one solution reachable by logic.

Marking empty cells

Most solvers use two kinds of mark: a filled square for cells that are definitely part of the picture, and a dot or cross for cells that are definitely empty. Marking empty cells is just as important as filling. Many deductions come from knowing where a run cannot go, and a cross is how you remember that.

The overlap technique

The overlap technique is the most important nonogram strategy and the usual way to begin. The idea: slide a run as far left as it can go, then as far right as it can go. Any cells covered in both positions must be filled, wherever the run really sits.

Take a row of 10 cells with the clue 7. Pushed fully left, the run covers cells 1–7. Pushed fully right, it covers cells 4–10. Cells 4, 5, 6 and 7 are covered either way, so you can fill those four cells right away.

A handy shortcut: in a line with a single clue, the number of guaranteed cells is twice the run length minus the line length, if that is positive. For 7 in 10 cells: 2 × 7 − 10 = 4. For 5 in 10 cells: 2 × 5 − 10 = 0, so overlap alone tells you nothing.

Overlap with several runs

The same method works with several numbers. Add up the runs plus one gap between each pair to get the minimum space they need. The difference between the line length and that minimum is the slack. Any run longer than the slack has guaranteed cells.

Example: 10 cells, clue 4 3. The minimum space is 4 + 1 + 3 = 8, so the slack is 2. Leftmost, the 4 sits in cells 1–4 and the 3 in cells 6–8. Rightmost, the 4 sits in cells 3–6 and the 3 in cells 8–10. The 4 is guaranteed to cover cells 3 and 4, and the 3 is guaranteed to cover cell 8.

When the slack is zero, the line is fully determined. A clue of 4 5 in a 10-cell row needs exactly 10 cells, so you can fill it straight away with one gap in cell 5.

Working from the edges

Filled cells near the border are powerful. If the first cell of a row is filled, it must belong to the first run, and that run must start there. With a first clue of 3, you can fill cells 1–3 and cross cell 4. The same logic works from the right or bottom edge with the last clue.

More generally, a filled cell close to an edge limits where its run can begin. If cell 2 is filled and the first clue is 4, the run covers cell 2 and therefore extends at least to cell 4, so cells 2–4 are filled whether it starts at cell 1 or cell 2.

Completing and crossing lines

• Finished lines: once all runs in a line are placed, cross every remaining cell.
• Too-small gaps: a gap between crosses that is shorter than any remaining run must be empty.
• Switch directions often: each new mark in a row may unlock its columns, and the other way round. Solving a nonogram is a steady back-and-forth between the two.

Multi-colour nonograms

Colour nonograms give each clue number a colour as well as a length. The rules change in one useful way: two neighbouring runs of different colours do not need a gap between them, while runs of the same colour still do. The overlap and edge techniques still apply, but you must track colours as well as lengths.

Nonograms and other logic puzzles

Nonograms share a lot with other grid deduction puzzles: you decide, cell by cell, whether something belongs there, and each decision constrains its row and column. Nurikabe and Tents have the same filled-or-empty flavour. Star Battle works similarly too, with stars instead of filled cells; the Star Battle strategy guide shows how overlap-style thinking carries over, or you can try a Star Battle puzzle right away. For more ideas, see our list of puzzles like Sudoku.