How to Solve Nonograms: Step-by-Step Techniques

September 15, 2026 · 4 min read

The numbers don't tell you the picture; they tell you where it can't be. This guide shows how to find the first square on an empty board and finish the puzzle without guessing, with examples you can solve right here.

What is a nonogram?

A nonogram is a logic puzzle in which you uncover a hidden picture on a grid using nothing but numbers. Each row has numbers on its left and each column has numbers on top. They give the lengths of the runs of consecutive filled squares in that line, in order from left to right and top to bottom. Two runs in the same line are always separated by at least one empty square.

If a row's clue is 3 1, that row contains a run of three filled squares, at least one gap, then a single filled square. The clue doesn't say where they start; working that out is the puzzle.

The quickest way to understand it is to play. The board below is a real puzzle with exactly one solution and no guessing required. Tap a square once to fill it, again to mark it empty.

The first technique: overlap

Where do you start on an empty board? By finding the squares a run must cover no matter where it slides.

Take a ten-square row with the clue 8. Pushed as far left as possible, the run covers squares 1–8; pushed as far right as possible, squares 3–10. Squares 3–8 are filled in both cases, so they're filled whichever placement is correct:

A quick rule: when a single run is longer than half the line, the number of certain squares is 2 × run − line length. For 6 that's two squares; for 4 it's zero, so on its own it tells you nothing:

The same idea works with several runs. When the runs plus their mandatory gaps fill the line exactly, the whole line is solved in one move:

Mark the empty squares

Solving a nonogram isn't only about finding filled squares. Marking a square you know is empty is just as valuable, because it narrows where runs can fit in the crossing line.

• A line with the clue 0 is empty from end to end.
• Once every run in a line is placed, mark the rest as empty.
• When a run reaches its full length, the squares at both ends must be empty.
• Squares no run can reach are empty too.

Most apps use a cross for this mark. Skipping it seems faster, but on large boards it forces you to remember what you already know, and that's where most mistakes come from.

Rows and columns together

When a row gives up everything it can, switch to the columns. A square newly fixed in a column opens a new deduction in its row, and the puzzle is solved by going back and forth.

In the 10×10 umbrella puzzle below, a single pass over the rows alone already fixes 26 squares. The third row's clue is 10 and the fourth's is 1 6 1: both determine their row completely. The lower rows say nothing on their own; the columns will solve them.

Now finish the same puzzle yourself:

Do you ever need to guess?

Not in a well-made nonogram. At every step, at least one square can be deduced for certain from some row or column. If you catch yourself thinking "let me fill this and see", either you missed a deduction or the puzzle is badly made.

The second happens more often than you'd think. A puzzle can have more than one solution, and it can even have exactly one solution yet still not be solvable by logic alone. We show how, with real examples, in nonograms that need guessing.