How to solve nonograms: the line techniques

A nonogram (also called picross, griddlers or Japanese crossword) is solved one line at a time. You never need to guess: if you study each row and column with the techniques below, the picture appears. This guide uses the same rules as the Stencil daily puzzle, and every Stencil picture can be solved with nothing more than what is written here.

The rules in one minute

The numbers beside a row or above a column give the lengths of the runs of filled squares in that line, in order. 3 1 means a run of three filled squares, then at least one empty square, then a run of one. 0 means the line is empty. Filled squares form the picture, and crossed squares are your notes for squares that must stay empty.

Technique 1: lines that are full or empty

Add the runs and the gaps between them: the clue 2 1 needs 2 + 1 + 1 = 4 squares. If that total equals the length of the line, the line is fully determined. A clue of 5 in a 5-square line fills every square, and a clue of 0 crosses every square. Start every puzzle by scanning for these.

Technique 2: overlap in long runs

Slide the run as far left as it goes, then as far right. Squares covered in both positions are certainly filled. In a 10-square line the clue 7 can start in squares 1 to 4, so squares 4 to 7 are filled whichever it is. The bigger the run compared with the free space, the more you learn. With several runs, do the same for each run using the total slack of the whole line.

Technique 3: edges and finished runs

If a filled square touches the edge of the grid and belongs to the first run, the whole first run is anchored there, so fill its remaining squares and cross the square after it. When a run is complete, cross the squares on both sides of it. Crossing is not busywork: crossed squares shrink the room left for the other runs, which creates new overlaps.

Technique 4: squares that nothing can reach

If the largest unplaced run is longer than a stretch of open squares between crosses, that stretch cannot hold it and can be crossed. In the same way, a square too far from any run that could still reach it is empty. Work from the ends of a line inwards.

Technique 5: bounce between rows and columns

Each square you settle helps two lines. After finishing a row, look at the columns it touches: the new filled and crossed squares are fresh information for them. When you feel stuck, re-read every line once more, because a square marked ten minutes ago may now complete an overlap. If a line really offers nothing, move on and come back.

A worked example

This 5 by 5 puzzle has row clues 3, 3, 3, 5, 5 and column clues 5, 5, 5, 2, 2.

1. Rows 4 and 5 have the clue 5 in a 5-square line, so both rows are completely filled (technique 1).
2. Columns 1, 2 and 3 have the clue 5 in 5 squares, so they are completely filled too.
3. Rows 1, 2 and 3 have the clue 3, and squares 1 to 3 are already filled, so the run is complete. Cross squares 4 and 5 in each (technique 3).
4. Columns 4 and 5 have the clue 2, which is already the two filled squares in rows 4 and 5. The puzzle is solved: a boot, three rows of leg above a two-square-wider foot.

When it will not budge

Paste the clues into the step-by-step nonogram solver to see which line makes the next deduction and why. Some hand-made puzzles, especially random ones, need a guess to finish or have several answers. The solver tells you when that is the case. Every Stencil picture is checked by two programs to have exactly one answer that line logic reaches, so on Stencil a stuck moment always means there is one more line to look at.