How Nonogram overlap works

Consider a line of 10 cells with a clue of 7. The earliest legal run fills cells 1 through 7, while the latest fills cells 4 through 10. Cells 4 through 7 are covered in both positions, so they must be filled. The cells near either edge remain unresolved because at least one legal placement leaves them empty.

Overlap never chooses the placement that looks most centered. It records only the intersection of all valid placements. The longer the run is relative to the available space, the larger that intersection becomes. A run longer than half the line always produces some overlap when no other marks restrict it.

For a clue such as 4 3, the run of four must appear before the run of three, with at least one empty cell between them. Build the earliest complete arrangement from the start of the line, including the required gap, then build the latest complete arrangement backward from the end. Compare the first run with the first run and the second with the second.

Do not merge filled areas from different groups into one overlap. A square covered by the first run in one layout and the second run in another is not guaranteed, because clue ownership changed. Each group's position must overlap with its own legal positions while the full sequence remains valid.

Existing filled cells can anchor a clue group. If a run of five must include a known filled square, discard any placement that misses it. Crosses work as hard boundaries: no run can pass through a crossed cell, so they may shorten the usable segment or force a group toward one side. Recompute earliest and latest positions inside the new limits.

A filled cell does not automatically tell you which clue group owns it when several groups remain. Test the complete clue order. If assigning the cell to one group leaves too little room for earlier or later groups, that assignment is impossible; the remaining assignment may create a much tighter overlap.

Overlap often creates a partial run rather than completing a clue. Once a partial run reaches the exact clue length, cross the cells immediately outside its ends. Separate groups cannot touch, so those boundary crosses are as certain as the filled run. They also divide the line into smaller segments for the remaining clues.

If a partial run is shorter than its clue, extend it only where every legal placement reaches. A run of five containing three connected fills may still extend on either side. Compare the leftmost and rightmost valid completions; cells shared by both extensions are safe to fill, while the uncertain endpoints stay open.

After marking overlap in one row, inspect every affected column. New fills can anchor column groups and new crosses can split them into smaller spaces. Follow those consequences before returning to the original row. Nonograms advance by transferring certainty between orientations, not by finishing every row in isolation.

When overlap yields nothing, choose a more constrained line, close completed runs, inspect edge anchors, and exclude segments too short for the remaining clues. Then try overlap again with the new boundaries. If a result depends on the expected picture rather than all legal clue layouts, it is a guess and should remain unmarked.