Nonogram guide: overlap, separators and certain empty cells
Every filled cell should follow from a row or column clue. Separate what is certain from what merely looks like part of a picture, then pass each deduction across the grid.
Back to the game →Translate the clues into runs
A clue lists consecutive filled runs in order. A line marked 3, 1 needs three filled cells, at least one empty separator, then one filled cell. Extra empty cells can go before, after or between the runs.
Add the run lengths and one mandatory separator between adjacent runs. If this equals the line length, the line is fixed. For five cells with clues 3, 1, the only arrangement is ■ ■ ■ × ■. A blank-looking cell is not automatically a proved empty cell.
Overlap the extreme placements
Imagine every run pushed as far left as the clues allow, then as far right as possible. Cells occupied by the same run in every legal placement must be filled. Existing crosses and filled cells can narrow the placements further.
For a single run of length k in n empty cells, overlap exists when 2k is greater than n. With a run of 3 in 5 cells, only the center overlaps. The four other cells remain undecided, not empty.
Worked example: prove the center first
The diagram lists all three placements for a run of 3 in a five-cell line. Compare each column of the diagram: only the third cell is filled in all three. Transfer that one certain fill to the puzzle.
Now inspect the perpendicular clue through that cell. A deduction in a row becomes evidence in a column. Alternate between the two axes instead of trying to finish every row before considering the columns.
Five cells, clue 3
The block of three can start in three places. Only the middle cell is filled in every placement. The other four cells are still undecided: do not mark them empty.
Use edges and completed runs to prove blanks
If a clue 3 touches the left edge with a known filled first cell, its run must fill cells 1–3; cell 4 must be empty. If a run is complete and its identity is certain, mark a separator at either end where a cell exists.
Do not put separators around every visible fragment. Two nearby filled cells may belong to the same unfinished run. Test whether connecting them would exceed the relevant clue or make the remaining runs impossible before deciding that the gap is empty.
Recover from a contradiction
If a line no longer fits its clues, revisit the last uncertain choice. Undo speculative fills instead of forcing a picture to look right. The game's check and hint controls can help you inspect a problem, but they should not replace reading the reason for a move.
Automatic crosses on a completed-looking line follow your current marks. They do not prove that an earlier guess was correct. Keep a routine: exact-fit lines, overlap, separators, crossing clues, then another scan. If nothing is forced, leave it undecided while examining another line.