How to Solve Nonograms: Rules, Notation and the Techniques That Work
A nonogram is a grid where the numbers beside each row and column tell you which cells to fill, and the filled cells form a picture. You solve it with a handful of line-by-line techniques, no guessing required. Here are the rules, every core technique with a concrete example, and a full 5x5 puzzle solved from start to finish.
The rules and how to read the clues
Every row and every column has a clue: a list of numbers. Each number is a block of consecutive filled cells in that line, and the blocks appear in the same order as the numbers, left to right for rows and top to bottom for columns.
Between two blocks there is at least one empty cell. There can also be empty cells before the first block and after the last one. A clue of "3 1 2" in a row of 10 means a block of three, then a gap, then a single cell, then a gap, then a block of two, with the exact positions left for you to work out.
A clue of "0", or an empty clue, means the whole line is empty. A well-made nonogram has exactly one solution, and you can reach it by logic alone.
- Fill a cell when you have proved it is part of a block.
- Mark a cell with a dot or an X when you have proved it is empty. Marking empties matters as much as filling: most deductions start from a known empty cell.
- Cross out or grey a clue number once its block is fully placed. It keeps your eye on the blocks that are still open.
Simple boxes: the overlap method
This is the technique that opens almost every puzzle. Take a row of 10 cells with the clue "7". If the block sits as far left as it can, it covers cells 1 to 7. As far right as it can, it covers cells 4 to 10. Cells 4 to 7 are filled in both positions, so they are filled in every position. Fill them.
The general version works for any clue. First add up the blocks plus one gap between each pair: that is the minimum length the clue needs. Subtract it from the line length to get the slack. Any block longer than the slack has certain cells: its length minus the slack, counted from the end of its leftmost position.
Example: a row of 15 with the clue "4 6 2". The minimum length is 4 + 6 + 2 + 2 gaps = 14, so the slack is 1. The block of 4 gets 3 certain cells (cells 2 to 4), the block of 6 gets 5 (cells 7 to 11) and the block of 2 gets 1 (cell 14). Nine cells from one line, before you have looked at anything else.
A block no longer than the slack gives nothing yet. That is why the biggest numbers in the biggest clues are the place to start.
Simple spaces and finished lines
Overlap tells you what must be filled. Simple spaces tell you what cannot be. Every block has a reach: the set of cells it could ever occupy. A cell that no block can reach is empty.
Example: a row of 10 with the clue "3" and cell 6 already filled. The block of 3 must include cell 6, so it starts at cell 4, 5 or 6 and can only cover cells 4 to 8. Cells 1 to 3 and 9 to 10 are empty.
The same idea finishes lines. The moment a line contains all of its blocks, every remaining unknown cell in it is empty. Mark them at once. Those new empties feed straight into the crossing columns, and that cross-feeding is how a nonogram unravels.
Forcing, glue and edge logic
Forcing: look at a stretch of unknown cells boxed in by empties or by the edge. If it is shorter than every block that could still go there, it stays empty. A two-cell gap in a row whose remaining clue is "3 4" can hold neither block, so cross it out.
Glue: a filled cell close to the edge pulls the first block toward it. In a row of 10 whose first clue is 4, suppose cell 3 is filled. That cell must belong to the first block, because nothing could fit before it. The block of 4 therefore starts at cell 1, 2 or 3, and in every case it covers cells 3 and 4. Fill cell 4.
Edge logic is glue at its strongest. If the very first cell of a line is filled, the first block starts there and is fully known: with a first clue of 4, fill cells 1 to 4 and mark cell 5 empty. The same applies from the right edge with the last clue, and from any confirmed empty cell that acts as a wall.
Joining and splitting
When two filled cells sit close together with unknown cells between them, ask whether they can belong to the same block.
Joining: a row with the single clue "5" has filled cells at 3 and 6. Both belong to the one block, so everything between them is filled too. Fill cells 4 and 5.
Splitting: a row with the clue "2 2" has filled cells at 3 and 5, with cell 4 unknown. Filling cell 4 would create a run of three, longer than any block in the clue. Cell 4 must be empty, which also tells you cell 3 ends the first block and cell 5 starts the second.
The test is always the same: if joining would make a block longer than the largest number that could reach both cells, split them. If both cells must belong to the same block, join them.
Line solving to completion
All the techniques above are shortcuts for one complete method. For any line, slide every block as far left as the known cells allow, then as far right as they allow, keeping the order and the gaps.
A cell covered by the same block in both arrangements is filled. A cell that lies after a block's rightmost position and before the next block's leftmost position is empty, and so is any cell before the first block's leftmost start or after the last block's rightmost end.
Run that on a line, then on every crossing line you changed, and repeat. Most published nonograms, including large ones, fall to this loop alone.
Very hard puzzles occasionally reach a point where no single line gives anything new. Then you test one cell: assume it is filled, follow the consequences, and if they lead to a contradiction, the cell is empty. This is still logic, not guessing, but it should be your last tool rather than your first.
A worked example: a 5x5 heart
Here is a complete puzzle you can draw on paper. Row clues, top to bottom: "1 1", "5", "5", "3", "1". Column clues, left to right: "2", "4", "4", "4", "2".
Step 1, full lines. Rows 2 and 3 have the clue "5" in a line of five, so both rows are completely filled.
Step 2, overlap. Row 4 has "3" in five cells, slack 2, so its middle cell (column 3) is filled. Columns 2, 3 and 4 each have "4" in five cells, slack 1, so rows 2 to 4 are filled in each of those columns.
Step 3, finished columns. Column 1 has the clue "2" and already holds filled cells in rows 2 and 3. That is its whole block, so rows 1, 4 and 5 of column 1 are empty. Column 5 works the same way.
Step 4, row 4. Columns 1 and 5 are now empty and columns 2 to 4 are filled. That is the block of 3, so row 4 is done.
Step 5, row 1. Its ends are empty, which leaves columns 2 to 4 for the clue "1 1". Two single blocks with a gap fit only one way: columns 2 and 4 filled, column 3 empty.
Step 6, the last cells. Column 2 now has rows 1 to 4 filled, its full block of 4, so row 5 is empty. Column 4 likewise. Column 3 is empty in row 1, so its block of 4 must be rows 2 to 5, which fills the bottom point of the heart. Row 5 reads "1", as it should.
Notice the rhythm: a big clue gives cells, the cells finish a crossing line, the finished line gives empties, and the empties finish the next line.
| Row | Clue | Solution (# filled, . empty) |
|---|---|---|
| 1 | 1 1 | . # . # . |
| 2 | 5 | # # # # # |
| 3 | 5 | # # # # # |
| 4 | 3 | . # # # . |
| 5 | 1 | . . # . . |
Common mistakes
Almost every stuck nonogram comes from one of a few habits. Fix these and your solve times drop quickly.
- Not marking empty cells. A filled cell is only half the information; the empties are what make glue, forcing and splitting possible.
- Forgetting the gap. Two blocks in a clue always need at least one empty cell between them, so "3 4" needs eight cells, not seven.
- Placing blocks out of order. The first number is always the leftmost or topmost block.
- Working one area to exhaustion. After every change, revisit the crossing lines; that is where the new information went.
- Guessing to break a stall. In a puzzle with a unique solution there is always a logical step. Re-run overlap with the cells you now know before testing anything.
- Ignoring small clues near edges. A "1" next to a filled edge cell often finishes a line instantly.
How to pick a puzzle size
Size changes the experience more than difficulty labels do. Larger grids have longer clues with more blocks, so the slack is bigger and overlap gives less at the start.
On a phone, 15x15 is comfortable, while 20x20 and up benefit from zoom and a clear way to mark empties. Nonoku, our free offline puzzle app for Android, runs from 5x5 to 25x25 for exactly that reason, with a hint that shows the next logical step.
| Size | Good for | What to expect |
|---|---|---|
| 5x5 | First puzzles | Learn the rules; often solved in a minute or two |
| 10x10 | Beginners | Overlap and finished lines do most of the work |
| 15x15 | Regular solvers | Glue, splitting and cross-checking become essential |
| 20x20 | Experienced solvers | Long clues with small slack; patience pays |
| 25x25 and up | Long sessions | Systematic line solving; marking empties is vital |
Other names for nonograms
The puzzle was invented in Japan in the late 1980s and spread under many names. The rules are the same whichever one a publisher uses.
| Name | Where you will see it |
|---|---|
| Nonogram | The general English name, after Non Ishida, one of the puzzle's Japanese creators |
| Griddlers | Common in the UK and among online communities |
| Hanjie | Popular in British newspapers and puzzle books |
| Picross | Nintendo's name for its video game series, short for picture crossword |
| Paint by numbers | Puzzle magazines and apps, not to be confused with the colouring hobby |
| Japanese crosswords | Widely used in Eastern Europe and Russia |
| Pic-a-Pix, Illust-Logic | Publisher brand names for the same puzzle |
Questions and answers
Do you ever have to guess in a nonogram?
Not in a well-made one. A good nonogram has a single solution that can be reached by logic. Most fall to line solving alone; the hardest may need you to test a cell and follow it to a contradiction, which is still a proof rather than a guess.
Where should I start a new nonogram?
Start with the lines whose clues add up closest to the line length, including the gaps. Those have the least slack, so overlap gives the most filled cells. Then follow every change into the crossing lines.
What is the difference between picross and a nonogram?
None in the rules. Picross is Nintendo's name for its nonogram games; nonogram, griddlers and hanjie are other names for the same puzzle.
How do colour nonograms differ?
Each number in a clue also has a colour. Blocks of the same colour still need at least one empty cell between them, but blocks of different colours may touch. The same overlap and edge techniques apply, colour by colour.
