How to solve nonograms

The rules

A nonogram (also called a Griddler, Hanjie or Paint by Numbers) is a grid of squares to shade. The numbers beside each row and above each column list the lengths of the shaded runs in that line, in order. Between runs there is at least one empty square. When every line matches its clue, a picture or pattern appears. Ours are symmetrical patterns.

1. The overlap method

Take one line on its own. Imagine pushing every run as far left as it will go, then as far right. Any square covered by the same run in both positions must be shaded, whatever the true answer is. In the strips below, “Before” is what you know and “After” is what you can be sure of.

A quick shortcut: add up the runs and the gaps between them. If the total is close to the length of the line, there will be overlap. In a line of 10, a single run of more than 5 always gives you some squares.

2. Mark empties too

Put a dot in every square you know is empty. A line whose clue is already satisfied can be dotted out completely, and squares too far from a known shaded square to belong to its run are empty. Dots are as useful as shading: they stop runs fitting where you might have guessed.

3. Let rows and columns take turns

Every square you settle in a row is new information for its column, and vice versa. Work through all the rows, then all the columns, and repeat. Each pass fixes a few more squares, and the pattern fills in. Our easy 10×10 puzzles take a few passes; the 20×20 ones take more.

4. Use the edges

A shaded square touching the edge of the grid must be the start of the first (or end of the last) run in that line, so you can extend it to that run's full length and put a dot after it.

Fair puzzles

Every nonogram on Puzzlebury is checked by a solver that works exactly as described here, one line at a time with no guessing. If you're stuck, there is always a line where the overlap method gives you something new.