How to Solve Nonograms

Nonograms, also known as Picross, Griddlers or Hanjie, can be solved by logic alone. This page walks through the basic techniques with diagrams. Every step uses only what a single row or column's clues guarantee, so no guessing is needed until the very last resort.

The rules and how to read the diagrams

The numbers to the left of each row and above each column are clues. Each clue is the length of a run of filled cells in that line, in order. "3 1" means a run of 3 cells, then at least one empty cell, then a run of 1 cell. Fill in every cell correctly and a picture appears.

The diagrams below show a single row of 10 cells, with the row's clue on the left.

1. Overlap: slide the blocks left and right

This is the technique you will use most. Imagine every block pushed as far left as it can go, then as far right as it can go. Cells covered by the same block in both positions are filled wherever the block really is.

You can also work it out with arithmetic. Slack = row length − (sum of the clues + number of clues − 1). Any clue longer than the slack fixes (clue − slack) cells in the middle of its block. Here the slack is 10 − 8 = 2, so 8 − 2 = 6 cells.

2. Lines that fit exactly, and zero lines

If the clues plus one empty cell between each pair of blocks add up to the row length, there is no slack and only one arrangement. A line whose clue is 0 (or has no clue) is entirely empty.

3. Mark cells no block can reach

Once you know a filled cell, work out how far its block could stretch. Cells that no block can reach are empty.

4. Grow from a filled cell near the edge

When you find a filled cell near an edge, ask which block it belongs to. If only one block can reach it, compare the positions where that block could include the cell; the cells they share are filled.

5. Close finished blocks

When a block reaches the length of its clue, the cells on both sides of it must be empty. Marking them makes the room left for the next block clear.

6. Empty the gaps too small for any block

If a gap between empty cells is shorter than every block that is still left, nothing fits in it. When the number of gaps matches the number of blocks, a row can be solved in one go.

7. Switch between rows and columns (5×5 walkthrough)

Every cell you determine in a row is a new clue for the column that crosses it. When the rows stop giving you anything, look at the columns, and vice versa. Repeating this is the heart of solving a nonogram.

8. When you get stuck: trial and error

If no row or column gives you a new cell, assume that one cell is filled and keep going. If some line ends up contradicting its clue, the assumption was wrong, so that cell must be empty.

Mark the cells you fill during a trial in a different color so that you can undo them. Try cells where the choice matters most, such as a cell that could be the end of a long block, to reach a contradiction sooner.

If a trial never leads to a contradiction and both choices can be completed, the puzzle may have more than one solution.

9. Color nonograms

In a color nonogram, each clue has a color and gives the length of a block of that color. Only one rule differs from black-and-white puzzles:

• Blocks of the same color need at least one empty cell between them, as in black and white.
• Blocks of different colors may touch with no gap.

Techniques 1–6 still work; just remember that a gap is only required between blocks of the same color. Where different colors sit side by side, the missing gap leaves more slack, so overlap fixes fewer cells.

Color puzzles also give you an extra kind of clue:

• A color that is not in a row's clue cannot appear anywhere in that row. Cross-check with the column clues to narrow down the colors each cell can take.
• Once a cell's only options are "empty" or one single color, treat it like a black-and-white cell.

10. Irregular nonograms

Irregular nonograms have boards that are not rectangles: some cells are holes that are not part of the puzzle. When a row or column is split by holes, each section between the holes has its own clue.

Treat each section as a short row of its own, and every technique above applies. The usual mistake is reading a clue as belonging to the wrong section, so first check where the section for each clue begins.