How to Solve a Nonogram: Read the Clues, Find Overlap, Mark Empty Cells
A complete first solve on a small grid, with screenshots from an interactive tutorial.
A nonogram can look like a wall of numbers until you know what each number measures. The clues do not tell you which squares to color directly. They tell you the lengths of consecutive filled runs in each row and column. You solve the grid by finding cells that must be filled or empty in every possible placement.
We will use the 4 × 4 tutorial board in my iOS app, Simon Tatham’s Logic Puzzles. It is small enough to see the logic without guessing, and the same rules apply to larger boards.
What do the numbers around a nonogram mean?
Read row clues from left to right and column clues from top to bottom. A clue of 3 means one run of three filled cells. A clue of 1 1 means two separate single filled cells, with at least one empty cell between them. A cell that is neither confirmed filled nor confirmed empty is still unknown.
Every row and column must agree at the same time. Do not use the apparent picture as a shortcut: in this app, generated Nonogram boards can form abstract patterns rather than recognizable drawings.
Caption: The actual tutorial starts with all cells unknown. Its third row reads 1 1; its second column reads 3.
Where should you make the first move?
Look for a long run in a short line. On this four-cell board, a run of three can occupy cells 1–3 or 2–4. Both possibilities include cells 2 and 3. Those two overlapping cells are guaranteed filled, even though the run’s exact position is not known yet.
The tutorial has a 3 in column 2 and another 3 in row 4. Fill the middle two cells of each. This is the overlap method: write down the extreme placements, then fill only their intersection.
Caption: A run of 3 in 4 cells always covers the two middle cells.
When can you mark a cell empty?
Once the tutorial’s bottom cell in column 3 is filled, that column has met its clue of 1. No other cell in column 3 can be filled. The tutorial asks you to long-press the cell in row 2, column 3 to mark it empty.
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Empty marks are useful evidence, not just tidying. They prevent a run from extending in the wrong direction and give crossing rows a new constraint.
Caption: The column already has its one filled cell, so the highlighted cell must be empty.
How do row and column clues work together?
Now inspect row 2. Its clue is 2, and the cell in column 2 is filled. The cell immediately to its right is empty, so the two-cell run cannot extend right. It must extend left into column 1. One column deduction has forced a row deduction.
Caption: The white empty mark blocks the right side; row 2’s run of two must extend left.
The same pattern continues: complete a run, exclude cells beyond it, then check the crossing lines again. In row 3, the clue 1 1 requires a gap between its two filled cells. If a neighboring square would join them into one run, that square is empty.
How do you know the puzzle is finished?
Check every row and column against its clue, including the order of separate runs. On the tutorial board, the final filled pattern satisfies all eight lines. Some unfilled squares remain gray in the app because you do not have to explicitly mark every empty square before it recognizes the solution. The tutorial then waits for you to acknowledge completion.
Caption: The completed 4 × 4 example. Its result is a logical pattern, not a promised picture of an object.
Try the method on your next board
Start with the longest clues, find cells shared by all placements, mark confirmed empties, and alternate between rows and columns. If a move depends on how you think the picture should look, pause and find a clue that proves it instead.
I built this guided example into Simon Tatham’s Logic Puzzles on the App Store. Open Nonogram, tap the book icon in the game header, and work through the tutorial on the board shown here. You can then start a fresh board and apply the same overlap and cross-checking method.
