How to solve a nonogram, step by step

On this page

1. Reading the clues
2. Start with lines that are already decided
3. Find the overlap
4. Let rows and columns trade information
5. Work from the edges
6. Mark what you rule out
7. Choosing a size

A nonogram is a picture hidden in a grid. The numbers beside each row and above each column tell you how the filled squares are grouped, and pure logic tells you where they go. You never need to guess. This guide walks through the reasoning in the order most solvers use it, from a first 5 × 5 grid to the habits that make a 15 × 15 puzzle manageable. You can print practice grids with answer keys from the nonogram maker.

Reading the clues

Each number is a run of filled squares in that line, and the runs come in the order the numbers are written: left to right for rows, top to bottom for columns. Between two runs there is always at least one empty square. A clue of 0 means the whole line stays empty.

Use a pencil. Fill a square when you are sure it is part of the picture, and mark a square with a dot or a light cross when you are sure it is empty. Both kinds of mark are information, and the dots are often what unlocks the next step.

Start with lines that are already decided

Some lines can be filled straight away. Add up the clue numbers, then add one for every gap between runs. If the total equals the length of the line, there is only one way to place the runs.

For example, a row of 10 with the clue 3 4 1 needs 3 + 4 + 1 squares plus two gaps, which is exactly 10. The row is fully decided. A clue of 0 is decided too: mark every square as empty.

Find the overlap

Most lines are not decided at once, but a long run still gives something away. Imagine the run pushed as far left as it can go, then as far right. Any square covered in both positions must be filled.

In a line of 10 with the clue 7, the run covers squares 1 to 7 when pushed left and squares 4 to 10 when pushed right. Squares 4, 5, 6 and 7 are covered either way, so you can fill them now. A quick way to count: the overlap is the run length minus the free space, here 7 − 3 = 4 squares.

The same trick works with several runs in one line. Push all of them to the left, then all of them to the right, and compare each run with its own copy.

Let rows and columns trade information

Every square belongs to one row and one column. When you fill or mark a square while working on a row, the column it sits in now has a new fact, and that may be enough to settle more of the column. Solving a nonogram is mostly this back-and-forth.

A good rhythm is:

1. Fill every decided line and every overlap you can find.
2. Go through the columns, using the squares the rows have given you.
3. Go back to the rows with what the columns have added.
4. Repeat until the picture is complete.

Work from the edges

The edges of the grid are a strong source of logic. If the first number of a row is 3 and the square touching the left edge is filled, that square must be the start of the 3, so the next two squares are filled and the square after them is empty.

Filled squares near an edge also limit where a run can begin. If a run of 4 must include a square two places from the edge, the run cannot reach past a certain point on the other side, and squares beyond that point belong to later runs or stay empty.

Mark what you rule out

Once a line has all its runs in place, mark the remaining squares as empty. When a gap between filled squares is too short for any run that could still go there, mark that gap empty as well. Beginners often skip the dots, but a line full of dots shows the remaining space clearly, and it shrinks the overlaps in the crossing lines.

Tip: When you are stuck, look for the line with the least free space. Short gaps and long clues leave little room, so they are the most likely to give up another square.

Choosing a size

A 5 × 5 grid is small enough to solve in a few minutes and is a good way to learn the overlap. A 10 × 10 grid is the classic size and needs every technique above. A 15 × 15 grid takes longer and rewards keeping your dots tidy.

Paperoom prints each puzzle with its clues and, if you choose, an answer key on a separate page, so you can check a finished picture or peek at one square when a grid refuses to move.