Nonogram overlap, one line at a time.
Compare every legal placement of a line's clues. If every placement fills a square, fill it. If every placement leaves it empty, mark it empty. When placements disagree, keep the square unknown.
These are monochrome Nonogram rules: each clue is a filled group, with at least one empty square between groups. Try your own line below, or follow the worked examples. If the clues are new to you, start with our 5 × 5 introduction.
Check a Nonogram line
For a monochrome row or column, enter its clues and any squares you already know. The helper compares every legal placement, keeping at least one empty square between groups.
This interactive check needs JavaScript. You can still read the worked examples below.
3 valid placements. 1 new filled square and 0 new empty squares.
What is certain
Fill: 3
Mark empty: None
Compare the possible placements
Every placement below follows the clues and your known marks. All 3 were checked for the certain squares above.
Placements 1–3 of 3.
Clue 3 in five squares: the middle is certain
The three filled squares must stay together. They can start at square 1, 2 or 3, giving these three possible arrangements:
The middle square, number 3, is filled in all three arrangements. The other squares change between filled and empty, so they remain undecided on your real puzzle. These diagrams are alternatives to compare, not three rows to copy into your grid.
Clues 2, 2 in five squares: an exact fit
Two filled squares, one required empty gap, and two more filled squares use all five spaces: 2 + 1 + 2 = 5. There is only one legal arrangement.
The empty square is as certain as the fills. Joining the two groups would make a run of four, which describes a different clue.
Clues 4, 3 in ten squares: keep the groups in order
The four-square group comes first, then at least one empty square, then the three-square group. The minimum is eight squares, leaving two more empty spaces to distribute before, between or after the groups. There are six possible arrangements:
Squares 3, 4 and 8 are filled in every arrangement. Every other square varies. Keeping the whole line in view preserves the order and gap between the groups.
A shortcut for one group in an unknown line
For one group of k filled squares in a line of n squares, with no known marks and a clue that fits, the number of guaranteed filled squares is:
max(0, 2 × k − n)
For 3 in 5, that is 2 × 3 − 5 = 1: the middle square. For 2 in 5, it is 0, so that clue alone does not force a filled square.
For several groups or a line with known marks, compare valid placements of the whole line. The other groups, their order, the gaps and the known marks all affect where a run can go.
When a line has no new deduction
A line can have several legal arrangements that share no new marks. Check a crossing row or column, carry its proven marks back, then try the line again. An unknown square is still open to either possibility.
If no arrangement fits, recheck the clue order, line length and known marks. The helper treats entered marks as facts; a mistaken mark elsewhere in the full puzzle can make an otherwise plausible line misleading.
To practice moving between rows and columns, follow the complete 5 × 5 lesson or the 10 × 10 worked puzzle. They show how individual line deductions fit into a complete picture.