How to solve a nonogram
A nonogram is a picture hidden in a grid. The numbers beside each row and above each column tell you the blocks of shaded squares in that line. Here is a complete solve of a small puzzle, one deduction at a time — the same three ideas solve every nonogram.
The puzzle
Five rows, five columns. The row clues are on the left, the column clues on top. Shaded squares are dark; a cross means "proved empty".
The solve, step by step
New squares in each step are in colour.
Rows 2 and 3: a full line
Both rows have the clue 5 in a row of 5 squares. A block of five fills the whole row, so every square in rows 2 and 3 is shaded.
Row 4: the overlap
Row 4 has a block of 3. Pushed as far left as it goes it covers squares 1–3; pushed right it covers 3–5. Square 3 is shaded either way — that is the overlap.
Columns 1 and 5: a block already placed
These columns have the clue 2, and rows 2 and 3 already give them two shaded squares side by side. That is the whole block, so the other three squares are crossed out.
Columns 2 and 4: overlap again
Clue 4 in a column of 5: the block covers rows 1–4 or rows 2–5. Rows 2, 3 and 4 are shaded in both — so row 4 gets two more shaded squares.
Row 1: two single blocks
Row 1 has 1 1, but its first and last squares are crossed out. Two single blocks with a gap between them need exactly three squares — squares 2, 3, 4 — so 2 and 4 are shaded and 3 is crossed out.
Finish the columns
Columns 2 and 4 now have their block of 4 (rows 1–4), so row 5 is crossed out. Column 3 cannot start in row 1, so its block of 4 is rows 2–5. The picture is a heart.
The three ideas
- Full lines. Add the blocks plus one gap between each. If the total equals the row length, the row is completely known.
- Overlap. Slide a block to both ends of the space it can use. Squares covered in both positions are shaded.
- Cross out. When a line has all its blocks, cross out the rest. Crosses are as useful as shading — they limit where blocks in the other direction can go.
On bigger grids you will also use edges (a shaded square next to the edge fixes where the first block sits) and gaps too small for any block. The nonogram guide covers these, and the row calculator shows every way a clue fits a row.
Try it yourself
The Nonogram game starts at 5×5 and goes up to large pictures. If you get stuck, the Nonogram Solver shows the next line to work on and why.
Questions
What do the numbers in a nonogram mean?
Each number is a block of that many shaded squares in a row, in order. 3 1 means a block of three, then at least one empty square, then a single shaded square.
Where should I start?
With the biggest clues. A clue that fills the row exactly, or more than half of it, always gives shaded squares by the overlap method.
Do I ever need to guess?
Not in a well-made nonogram. Every puzzle in the Nonogram game can be solved one line at a time, like this example.
What is the overlap method?
Push a block as far left as it can go, then as far right. Any square covered both times must be shaded. It works for whole clues too: add the blocks and the gaps, and compare with the row length.