How to solve a nonogram: strategy for beginners, no guessing

You can solve every nonogram by proof, and a small set of moves covers nearly all of it. Learn these in order, and reach for the next one only when the one before has nothing left to give.

1. Overlap

Take a line and push its runs as far left as they go, then as far right. Any square a run covers in both positions is filled wherever the run truly sits. A run of six in a ten-wide line covers squares five and six both ways, so you can fill them. The longer the run compared to the line, the more it gives you. A run as long as the whole line fills it outright, and a 0 empties it.

Pushed left 6
Pushed right 6
Both ways 6
A ten-square line with the clue 6. Pushed left the run covers squares one to six, pushed right squares five to ten. Squares five and six are covered both ways, so they are filled.

Overlap works with several runs too. Push them all left, push them all right, and compare run by run.

2. Edges

A filled square at the end of a line belongs to the first or last run, so that run extends inward from the edge by its full length, and the square after it is empty. The same holds for a filled square next to a known empty one: the run touching it can't cross the empty square, so count from there.

Known 3 2
Counted in 3 2 ·
A line with the clue 3 2 whose first square is filled. The first run is three long, so squares two and three are filled too, and square four is empty.

3. Gaps too small to fill

A stretch of unknown squares between two empties that is shorter than every run still to place can't hold anything. Mark it empty. This move is easy to miss, and it clears a lot of a grid late in a solve.

Known 4 · ·
Too small 4 · · · ·
A line with the clue 4 and two known empty squares at positions three and six. The two unknown squares between them cannot hold a run of four, so they are empty.

4. Finished lines

When a line holds every square its numbers call for, everything left in it is empty. When you've placed every run but one, the remaining unknowns belong to that run or to nothing. Cross a line off the moment it's done, and the board stays readable.

Known 2 1
Finished 2 1 · · · · · · ·
A line with the clue 2 1 where both runs are already placed. Every other square is empty.

5. Work the crossings

A square settled in a row is a square settled in a column. After each move, look at the lines that cross the squares you changed. Most of a solve is this loop: one line gives a square, the crossing line uses it, and so on around the grid.

When nothing moves

If you've exhausted every line, the puzzle may need a longer argument: assume a square is filled, follow the consequences a few steps, and if they contradict a clue, the square is empty. Well-made puzzles rarely need this, and the ones you play in Nounogram never do. When you ask for a hint, it first tells you what kind of move to look for, then which line, and gives you the answer only if you ask for it.

The same moves, with words

In a Nounogram, the empty squares hold letters, and you spell a word into every run of letter squares. That gives you a sixth move: a word from the list that fits only one place on the board, by its length or by a letter it shares with a word you've already placed. Each word you place proves the solids on both ends of it, and each solid you prove rules out words. The two kinds of clue narrow each other until the grid is done.

Try it on today's easy puzzle, which is free, or play the tutorial first. Happy puzzling!