How to solve nonograms, and how we make every picture guess-free

A nonogram is a picture hidden in a grid. The numbers beside each row and above each column tell you how many squares to fill in and in what groups. Fill the right ones and a picture appears: a heart, a ship, a cup of coffee. Nonograms are also known as Picross, Griddlers, Hanjie and paint-by-numbers, and they are one of the few logic puzzles that reward you with a drawing at the end. Here is how to solve them, and how we make sure every picture on Nonograms.gg can be solved without a single guess.

How to read nonogram clues

Each clue lists the runs of filled squares in its line, in order. A clue of 3 1 means three filled squares side by side, then at least one empty square, then one more filled square. How big the gaps are is up to you to work out, and that is the whole puzzle. A clue of 0 means the line is completely empty.

In the heart above, the top row reads 2 2: two runs of two with at least one empty square between them. The second row reads 4 4, and the gap in its middle is the dip at the top of the heart. The last row reads 0, so it stays empty.

How to solve a nonogram, step by step

The most useful trick for beginners is the overlap. Take a row of ten squares with a clue of 8. Push the run as far left as it will go, then as far right. Six squares in the middle are covered both times, so they must be filled, whatever the rest of the puzzle says.

The overlap method on a single 10-square line with a clue of 8. The six shaded squares are certain.

The same idea works with several runs: slide all of them to one end, then to the other, and any square covered by the same run both times is filled. From there, the game becomes a conversation between rows and columns. Each square you settle gives the crossing line one more fact, and that line may now be able to prove something new.

• Start with the biggest numbers. Long runs have the fewest possible positions, so they give away squares first.
• Clear the zeros. A clue of 0 means the whole line is empty. Cross it out straight away, and a full-length clue fills its line in one go.
• Work from the edges. A filled square touching the edge must be the start of a run, so the rest of that run follows from it.
• Cross out as you go. Once a line has all its runs, mark every remaining square as empty. Those marks become clues for the lines that cross them.
• Switch between rows and columns. Every square you settle in a row is new information for a column. Most progress comes from going back and forth.

Why you never have to guess

Some nonograms can only be finished by trying a square and seeing whether it leads to a contradiction. Others have two different pictures that fit the same clues, so no amount of thinking can tell you which one the setter meant. Both spoil the puzzle. Our rule is simple: every square must follow from the clues of a single row or column, one line at a time. If a puzzle can be finished that way, it also has exactly one solution, because every square was forced. We wrote about the same idea for another game in why every Star Battle puzzle has a single solution.

How we turn emoji into puzzles

1. 1Draw the emoji large. Every picture starts as an emoji from Noto Emoji, an open-source emoji font. The shape is drawn at high resolution and cropped to a square.
2. 2Shrink it to the grid. The drawing is scaled down to 10×10 or 15×15 squares. We try several cut-off points for how much ink a square needs to count as filled, plus a solid silhouette version with the inner holes filled in.
3. 3Keep only real pictures. Between about a third and two thirds of the squares must be filled. Grids with too many empty lines or with all four corners filled are dropped, and so is any picture that differs from one already kept by less than one square in ten.
4. 4Solve it one line at a time. A solver works through the rows and columns using only what each single line proves, exactly the way you would. If it cannot fill every square, the version is thrown away and the next one is tried.

Some kinds of emoji simply do not survive being shrunk to a hundred squares. Clocks turn into circles, most people and gestures turn into blobs, and flags lose everything that makes them flags, so we leave those categories out and limit how many faces are used. The Easy 5×5 pictures are drawn by hand instead, because five squares is too small to shrink anything into, and they go through the same solver.

For the daily puzzle we pick the 400 cleanest 10×10 pictures, the ones with the smoothest outlines, and order them so the same kind of picture does not come up within a few days of itself.

Three sizes and a daily picture

The daily puzzle is one 10×10 picture, the same for everyone on the same date, and a new one arrives at midnight in your time zone. Unlimited mode lets you keep going with Easy 5×5, Medium 10×10 or Hard 15×15 grids. You can drag to fill several squares at once, mark squares you know are empty with an ✕ (right-click also works, and X switches tools), and undo with Ctrl+Z. If you like a safety net, the Show mistakes setting turns wrongly filled squares red.

The game speaks seven languages: English, French, German, Italian, Spanish, Portuguese and Dutch. The grids are the same everywhere, and each picture carries its own name in your language, which is revealed once you solve it. There is more about the game on our Nonograms page.

Try it yourself

Today’s picture is waiting at nonograms.gg. Look for the biggest number on the board, use the overlap, and let the rows and columns do the rest.