How to solve a nonogram

Five minutes · four boards you can play

1. The rules on one card
2. Reading the numbers
3. Overlap
4. Several numbers and gaps
5. Rows help columns
6. Habits that keep you moving
7. The hand before you

The rules on one card

• Each number is a run of painted cells in that row or column.
• Several numbers stay in order, with at least one empty cell between runs.
• 0 means the line is empty. Mark cells you know are empty with X.
• Every square can be solved by reading lines alone. You never need to guess.

On the boards below, tap a cell to paint it and tap again to clear it. Hold a cell (or right-click it) to mark it X. A number fades out once its run is complete, so you can see at a glance what is left.

1. Reading the numbers

Start with the lines that leave no choice. A run as long as the line paints the whole line, and a 0 empties it. Then look at what those cells tell the lines that cross them.

2. Overlap

A long run can slide only a little. Push it as far up (or left) as it goes, then as far down (or right): the cells it covers in both positions are painted whichever way it really sits. The quick count: slack = line length − run length. Every cell with at least that many cells between it and each end is painted. A run of 4 in 5 cells has a slack of 1, so the middle three are certain; a 7 in a line of 10 has a slack of 3, so the middle four are certain.

3. Several numbers and gaps

With several numbers, add them up and add one empty cell between each pair. If the total equals the line length, there is exactly one way to place them: 1 1 1 needs 1+1+1 plus two gaps, which is 5. If the total is a little shorter, overlap still works on the whole group: slide everything left, then everything right, and paint the cells that the same run covers both times.

4. Rows help columns

Nonograms are solved by going back and forth. Every cell you paint or cross out is new information for the line that crosses it, and that line may now be able to decide more cells, which help other rows in turn. On a 10×10 square, a typical solve visits each line two or three times.

Habits that keep you moving

• Cross out the ends of a finished run. When a run is complete, the cells on both sides of it must be empty. Mark them: an X is as useful a clue as paint.
• Work from the edges. A painted cell next to the edge (or next to an X) must be the start of a run. If the first number is 3, the next two cells are painted too.
• Rule out cells no run can reach. If the only run is 2 and a painted cell sits in the middle of the line, every cell more than one step from it is empty.
• Check the faded numbers. When every number of a line has faded, the line is done: cross out what is left (Many Hands does this for you).
• Stuck? Look for the line with the most cells already known. It usually has the least freedom left. On these boards, Show me points at the line that decides the most cells right now.

The hand before you

A picture cut from a painting is not always solvable from its numbers alone. When it isn't, the square ships with a few cells already painted by "the hand before you", shown with a pink dot. They are locked, and they are exactly enough to make the rest solvable by line logic. If you submit a wrong answer three times in the app, a previous hand paints one more row for you; you can also Borrow a row at any time.