How to Solve Nonograms

Published and updated September 14, 2026 · Written and illustrated by Cmirai, developer of the nonogram solver app Nonograver

A nonogram is a puzzle in which you fill in cells using the numbers beside each row and column, revealing a hidden picture. It is also known as Picross, Griddlers, Hanjie or Paint by Numbers. This page explains the basic techniques for solving nonograms by hand, with diagrams, for beginners. The basic techniques use only what a single row or column's clues guarantee, so they never require guessing.

What is a nonogram?

A nonogram is a logic puzzle in which you decide which cells of a grid to fill, using the numbers to the left of each row and above each column, until a picture appears. Tetsuya Nishio and Non Ishida each invented it independently in Japan around 1988. The name "nonogram" comes from Non Ishida. It was given when the British newspaper The Sunday Telegraph began publishing Ishida's puzzles in 1990, and the puzzle spread abroad from there. Publishers and games use different names, but the rules are always the same.

The rules and how to read the diagrams

There are only three rules. On this page, a row or a column is called a line.

1. Each number (clue) is the length of a run of consecutive filled cells in that row or column.
2. When a line has several clues, the blocks appear in that order, left to right or top to bottom.
3. There is at least one empty cell between two blocks.

Check them against a finished picture. In the 5×5 heart below, the clue "1 1" on the first row means a 1-cell block, a gap, then another 1-cell block, and the "5" on the second row means all five cells are filled. The "4" above the second column means four consecutive filled cells from the top.

The diagrams for techniques 1–10 show a single row of 10 cells taken from a grid, with the row's clue on the left. Techniques 11 and 12 look at rows and columns together, so their diagrams use a 5×5 grid. Cells known to be empty are marked with an X (×).

How solving works, in three steps

1. Find the lines where some cells are certain, and fill them in. Take the lines with large clues and slide the blocks left and right (technique 1). Finish lines that fit exactly and lines with a clue of 0 first (technique 2).
2. Use what you know, switching between rows and columns. A filled cell tells you which cells no block can reach (technique 3); a filled cell near the edge, or two filled cells that must share a block, tell you how the block continues (techniques 4 and 5). Close finished blocks (technique 6) and empty gaps that are too small (technique 7). Every new cell in a row is a new clue for its column (walkthrough).
3. When no line moves, use the advanced techniques, and trial and error last. Try the techniques that compare arrangements (techniques 8–12). If they do not help, assume one cell is filled, keep going, and mark it empty if you hit a contradiction (technique 13). Most puzzles are solved before you get here.

If you are new to nonograms, techniques 1–7 and the walkthrough are enough to solve most 10×10 puzzles. Read from technique 8 onward when you get stuck.

Technique 1: Overlap, slide the blocks left and right

Push the blocks as far left as they go, then as far right. Cells covered by the same block both times are filled.

This is the technique you will use most. Imagine every block pushed as far left as it can go, then as far right as it can go. Cells covered by the same block in both positions are filled wherever the block really is.

You can also work it out with arithmetic. Slack = line length − (sum of the clues + number of clues − 1). Slack is sometimes called freedom. Any clue larger than the slack fixes (clue − slack) cells in the middle of its block. Here the slack is 10 − 8 = 2, so 8 − 2 = 6 cells are fixed.

Which line to start with

Overlap fixes (clue − slack) cells in each block, and nothing if that is zero or less. So start with rows and columns that have large clues: the larger the clue and the smaller the slack, the more cells you get at once. For a row of 10 cells:

• "7": the slack is 3, so 7 − 3 = 4 cells are fixed.
• "2 5": the slack is 10 − (2 + 5 + 1) = 2. Three cells of the 5 are fixed; nothing of the 2 is fixed yet.
• "3": the slack is 7. The clue is smaller than the slack, so nothing is fixed yet.

Many clues alone are not enough. "1 1 1 1 1" in a row of 10 has a slack of only 1, but every clue is 1, so overlap fixes nothing.

Rule of thumb: any clue larger than half the line length fixes at least one cell.

Technique 2: Lines that fit exactly, and zero lines

If the clues plus the gaps between them add up to the line length, there is only one arrangement. A line with the clue 0 is entirely empty.

If the clues plus one empty cell between each pair of blocks add up to the line length, there is no slack and only one arrangement. A line whose clue is 0 (or that has no clue) is entirely empty. Finish both kinds first: they hand a lot of information to the crossing lines at once.

Technique 3: Mark cells no block can reach

Once you know a filled cell, work out how far its block could stretch. Cells no block can reach are empty.

Once you know a filled cell, work out how far its block could stretch. Cells that no block can reach are empty.

Technique 4: Grow from a filled cell near the edge

If only one block can reach a filled cell near the edge, fill the cells that block must cover.

When you find a filled cell near an edge, ask which block it belongs to. If only one block can reach it, compare the positions where that block could include the cell; the cells they share are filled.

Technique 5: Join separated filled cells

If two separated filled cells must belong to the same block, fill everything between them.

Sometimes you know two filled cells some distance apart. If only one block can reach both, they belong to the same block. A block is continuous, so every cell between them is filled. The block's length then also tells you how far it can extend on either side (technique 3).

Technique 6: Close finished blocks

When a block you know belongs to a clue reaches that clue's length, the cells on both sides are empty.

When a block reaches the length of its clue, the cells on both sides of it must be empty. Marking them shows how much room is left for the next block. Forgetting these marks is the most common reason for getting stuck.

The condition is that you know which clue the block belongs to. In a line with the clue "2 3", a run of two filled cells might still be part of the "3", so you cannot close it yet. A block as long as the largest clue in its line cannot be part of a longer block, so you can close it right away.

Technique 7: Empty the gaps too small for any block

If no remaining block fits in a gap between empty cells, the whole gap is empty.

If a gap between empty cells is shorter than every block that is still left, nothing fits in it. If each remaining gap can hold only one particular block and fits it exactly, the whole line is decided at once.

Switch between rows and columns (5×5 walkthrough)

Every cell you determine in a row is a new clue for the column that crosses it. When the rows stop giving you anything, look at the columns, and vice versa. Repeating this is the heart of solving a nonogram. Let's solve the heart shown in the rules section, starting from an empty grid.

Advanced techniques: when you get stuck

Techniques 1–7 use only a line's clue and the cells you already know. If no row or column moves, try the advanced techniques below, in order. The higher the number, the more work it takes.

Technique 8: Mark cells that would make a block too long

If filling a cell would make a run that no block in the clue can hold, the cell is empty.

Filling a cell next to a filled cell, or between two filled cells, joins them into a longer run. If none of the line's blocks can hold a run that long, you cannot fill that cell, so mark it empty. A block can fail to hold it because no clue number is long enough, or because a long enough clue cannot reach that far.

Adding just one cell next to a filled cell works the same way. The order of the clues helps too.

Technique 6 is a special case: once a block has reached the length of its clue, filling either neighbor would always make it too long.

Technique 9: Overlap again in the narrowed range

When Xs or filled cells narrow the range a block can occupy, compare its leftmost and rightmost positions again within the narrowed range.

Technique 1 compares positions using the clue numbers alone. Once Xs appear on the board, the range a block can occupy shrinks. Compare the left and right positions again inside the narrowed range, and a block that fixed nothing at first may now overlap itself. Try this again on a line each time it gets a new X.

If the range is exactly as long as the block, the whole block is filled.

Technique 10: Compare every arrangement

When nothing above decides a cell, write out every arrangement of the line that fits its clue and fix the cells that are the same in all of them.

Throw out the arrangements that clash with the filled cells and Xs first. Then compare what is left: a cell that is filled in all of them is filled, and a cell that is empty in all of them is an X. Techniques 1–9 are shortcuts for this method. Use it when only a few arrangements remain; when there are many, try techniques 1–9 first.

Technique 11: Match a row's and a column's colors (color puzzles)

In a color puzzle, if only one color fits both what the row alone allows and what the column alone allows, the cell takes that color.

In a color puzzle, a cell can still have several possible colors (plus empty). List what the row clue alone allows, list what the column clue alone allows, and keep only what is in both. If exactly one is left, the cell is decided. In a black-and-white puzzle, an undecided cell is always "filled or empty" for both the row and the column, so this technique never applies.

Technique 12: Think about two lines together

Take two rows (or columns) that each have only a few arrangements. An arrangement is impossible if, combined with every arrangement of the other row, some crossing column clue no longer fits. Cells that are the same in the remaining arrangements are decided.

Sometimes one row or column is not enough, but two rows together decide a cell. Write out the arrangements that fit each row (technique 10). Combine them one pair at a time, and place the cells of that pair into the columns they cross. If a column clue no longer fits, that pair cannot happen. An arrangement that fails with every arrangement of the other row cannot be the right one, so cross it out; the cells that are the same in the remaining arrangements are decided.

With many arrangements the combinations pile up, so use this on rows that each have only a few. You only check one crossing column at a time and never carry the result on to further rows or columns.

Technique 13: When you get stuck, trial and error

When no row or column moves, assume one cell is filled and keep going. If you reach a contradiction, that cell is empty.

If no row or column gives you a new cell, even after technique 12, assume that one cell is filled and keep going. If some line ends up contradicting its clue, the assumption was wrong, so that cell must be empty. This is also called bifurcation or proof by contradiction.

Mark the cells you fill during a trial in a different color so that you can undo them. Solve mode in Nonograver has trial placements that show those cells with a separate mark and undo them in one go. Try cells where the choice matters most, such as a cell that could be the end of a long block, to reach a contradiction sooner.

A trial often runs without any contradiction. If you can fill in the whole grid that way and every clue is satisfied, you have found the answer. If the trial stalls instead, undo it and try a different cell.

If assuming the same cell filled and assuming it empty both lead to a complete picture without a contradiction, the puzzle has more than one solution.

Tips for solving large puzzles faster

Above 15×15 the techniques are the same, but where you look makes a big difference to speed.

1. Start with the largest clues. Lines where many cells are fixed at once hand information to the crossing lines. You do not need to go through every line in order.
2. Close a block the moment it is finished. If you leave the Xs for later, you will forget them and get stuck.
3. Count with the bold lines every five cells. Read "cell 7" as "5 + 2" instead of counting one by one, and add up clues in groups of five and ten.
4. Only recheck the lines where a cell was just determined. If a row gave you three new cells, look at those three columns. Scanning the whole grid again and again wastes time.
5. When stuck, look for missing Xs and misread clues first. Trial and error comes after that.

Common mistakes

• Forgetting the Xs on both sides of a finished block. This causes most dead ends (technique 6).
• Overlapping different blocks. Only cells covered by the same block in the left and right positions are fixed (technique 1).
• Forgetting the gaps between blocks. "1 1" needs at least 3 cells, and "3 4" needs at least 8.
• Reading clues in the wrong order. Rows go left to right, columns top to bottom.
• Assuming a filled cell belongs to a particular clue. If you cannot tell which clue a block belongs to, you can neither extend it nor close it yet.
• In color puzzles, leaving a gap between different colors. Gaps are only required between blocks of the same color (color nonograms).
• In irregular puzzles, reading a clue that belongs to another section. Each section between holes has its own clue (irregular nonograms).

Color nonograms

In a color nonogram, each clue has a color and gives the length of a block of that color. Only one rule differs from black-and-white puzzles:

• Blocks of the same color need at least one empty cell between them, as in black and white.
• Blocks of different colors may touch with no gap.

Techniques 1–10, 12 and 13 still work (technique 11 is only for color puzzles); just remember that a gap is only required between blocks of the same color. Where different colors sit side by side, the missing gap leaves more slack, so overlap fixes fewer cells.

Color puzzles also give you extra kinds of clues:

• A color that is not in a row's clue cannot appear anywhere in that row. Cross-check with the column clues to narrow down the colors each cell can take.
• Once a cell's only options are "empty" or a single color, treat it like a black-and-white cell.
• Consider one color at a time and ask where blocks of that color could go. Some cells are decided this way before the black-and-white techniques get to them.
• If only one color fits both what the row alone allows and what the column alone allows, the cell is decided (technique 11).

Irregular nonograms

Irregular nonograms have boards that are not rectangles: some cells are holes that are not part of the puzzle. When a row or column is split by holes, each section between the holes usually has its own clue.

Treat each section as a short row of its own, and every technique above applies. Sections are often short, so lines that fit exactly (technique 2) are more common than in rectangular puzzles, which gives you easy places to start. The usual mistake is reading a clue as belonging to the wrong section, so first check where the section for each clue begins.

Cheat sheet

All the techniques in one table, to keep beside you while you solve the practice puzzles.

Practice puzzles (tap to solve)

Try the techniques above. Each tap cycles a cell through filled → empty (×) → unknown. On a computer, right-click toggles the × mark. Fill in every correct cell and a message tells you the puzzle is solved.

Puzzle 1: Beginner (5×5)

Start with the "5" row, then switch between rows and columns.

Puzzle 2: Easy (10×10)

One column has the clue "0". Start with the large clues. No trial and error is needed.

Puzzle 3: Hard (10×10, advanced techniques)

Techniques 1–7 alone will stall partway. Try technique 9 and technique 12; trial and error (technique 13) works too. The puzzle has exactly one solution.