How to Solve Nonograms (Picross): The Overlap Method

Updated June 2026

A nonogram — also called picross or a griddler — hides a picture behind number clues. Each clue lists the lengths of the filled runs in a line, and from those alone you reconstruct the image. It feels like it should need guessing, but it almost never does: a few line techniques, led by the overlap method, force cell after cell with certainty.

Reading the clues

Each row and column has a sequence of numbers. They give, in order, the lengths of the consecutive filled blocks in that line, with at least one empty cell between blocks. A row clued "4 2" means a run of four filled cells, then a gap of one or more empty cells, then a run of two — reading left to right. The clue tells you the lengths and the order, but not the positions; your job is to pin the positions down.

The overlap method — the heart of it

This is the single most important technique, and it works before you have filled anything. Take a line and imagine pushing each run as far left as it will go, then imagine pushing every run as far right as it will go. Any cell that is filled in both the leftmost and the rightmost arrangement is filled in the real solution too — there is no way to place the run that avoids it.

The rule of thumb: in a line of length L, a single run of size k forces filled cells whenever k is more than half of L. Concretely, the guaranteed overlap is the middle (2k − L) cells. On a line of 10 with a clue of 8, the run can start at column 1 or column 3 at the extremes, and columns 3 through 8 — the six cells in the middle — are filled no matter what. Big clues relative to the line are gold; fill their overlaps immediately across the whole grid.

Work the edges

Edges give away free information. If a line's first clue is, say, 3 and the very first cell is already filled, then the run must start exactly there: cells 1, 2, and 3 are filled, and cell 4 is empty (it caps the run). The same logic mirrors on the right edge. Any time you know where a run begins or ends, you can often place the entire run and the gap that follows it.

Mark the empties with X

Beginners only fill cells; strong solvers are just as eager to mark cells that must be empty, usually with a small X. Empty marks are not decoration — they actively drive the solve. Once a run is complete, the cells on either side of it are empty. Once a clue's total filled count is all placed in a line, every other cell in that line is empty. Those X marks then shrink the room available to the perpendicular clues, which creates new overlaps you could not see before.

Alternate between rows and columns

Nonograms are solved by ping-ponging. Squeeze every certainty out of the rows, then turn to the columns and do the same; the cells you filled and X'd from the rows give the columns new constraints, and vice versa. A cell you proved filled from a row's overlap might complete a column's run, which marks new empties, which unlocks another row. Keep cycling and the picture emerges.

Counting within a line

When a line is partly done, recount. Add up the clue numbers plus the minimum one-cell gaps between them — that is the smallest width the runs can occupy. Compare it to the space actually left. If they are equal, the line is fully forced and you can fill it completely. If a particular run has only one position left that fits around the cells you have already placed, put it there.

A reliable routine

1. Sweep every row and column for overlaps and fill the guaranteed middle cells.
2. Resolve edges where a run is pinned to the border.
3. X out every cell you can prove empty — beside finished runs and across completed lines.
4. Alternate rows and columns, re-checking overlaps as new X marks appear.
5. Use the count test on nearly-full lines to finish them.

A proper nonogram has one unique picture reachable by logic, so resist guessing — if a line stalls, the perpendicular clues almost certainly hold the cell you need. The reward is watching an abstract grid of numbers resolve into a recognisable image.