Solve a Nonogram by keeping only line arrangements that satisfy its ordered run clues, then using their shared filled or empty squares. Recheck crossing rows and columns after every deduction. This method starts from constraints, so it does not require guessing the picture the puzzle is supposed to show.
| 5 | 1 1 | 1 1 1 | 1 1 | 5 | |
|---|---|---|---|---|---|
| 5 | |||||
| 1 1 | |||||
| 1 1 1 | |||||
| 1 1 | |||||
| 5 |
The game is paused.
Fill cells to match each row and column’s clue groups in order. Leave at least one empty cell between separate groups. A 0 means the whole line is empty. Select Fill or Mark empty, then select a cell. Select it again with the same tool to clear the mark. Arrow keys move through the board; Enter or Space applies the tool. These three 5 × 5 puzzles do not save progress when you leave.
Add the run lengths and the required single gaps between consecutive runs. A clue of 2, 1, 2 needs at least seven squares: five filled and two separating gaps. If the line has exactly seven squares, its arrangement is forced. If it has more, the extra space allows the runs to shift or the gaps to grow.
Never omit the separators when counting. A clue of 1, 1, 1 needs five positions, not three. This simple calculation can expose a contradiction early: if your existing empty marks leave too little room for the required runs, at least one of those marks or an earlier assumption must be reconsidered.
For a single run of four in a six-square line, its leftmost placement covers 1–4 and its rightmost covers 3–6. Positions 3 and 4 are filled in every possible placement. Mark those two as proven while leaving the ends unresolved.
For multiple runs, keep their order and gaps while considering placements. The leftmost and rightmost arrangements must both obey existing filled and empty squares. A rough sketch that lets two runs touch is not a valid possibility. Only intersections of valid arrangements support a deduction; visual symmetry by itself does not.
A proven empty square prevents a filled run from crossing it. That can restrict a run to one segment of the line or divide several runs between segments. Compare the available lengths on each side with the clue requirements before deciding which groups belong where.
Suppose a run of three must lie within a segment containing exactly three available squares. Those squares are all filled, provided the assignment of that run to the segment is itself established. Do not skip that qualification: when two segments could both host the same run, you still need another constraint to choose between them.
If you have located a complete run, mark the required gap beyond it where the clue permits. A visible block of two filled squares might be the entire run for a clue of 2, or part of a longer run for a clue of 4. Determine which interpretation is supported before marking its ends empty.
Two visible groups in a line are not automatically two separate clue runs. Unresolved squares between them might eventually join them. Keep the clue order, known gaps, and maximum possible lengths in view. This avoids locking a line into a separation that the puzzle never required.
Every square belongs to a row and a column. A new filled square may force a column’s run to extend; a new gap may exclude its only remaining alternative. After changing a line, inspect its crossings instead of trying to complete one row in isolation while ignoring what it does to the rest of the board.
If no forced step appears, record the alternatives instead of committing to a picture. The small board supports line-logic practice but does not preserve an unfinished session across reloads. Before leaving, decide whether to continue now or return to a fresh puzzle later. On the larger 10 × 10 board, the same ordered-run and gap rules apply to longer lines. An entry is justified only when both its row and its column allow it.
The sum of the runs plus two required gaps, one between each neighboring pair.
Squares filled in every valid placement of a run or set of runs.
No. Unresolved squares may still join them unless a proven gap separates them.
A row must also agree with every crossing column; both sets of clues constrain the same squares.
No. The method described uses line constraints and their consequences.