To solve a nonogram, work on one row or column at a time and only mark squares you can prove. Start with overlap: a block that's longer than half its free space always covers the middle. Then cross out squares no block can use, push blocks in from the edges, join or split nearby filled squares, and keep switching between rows and columns, because every square you settle is a new clue for the line that crosses it. A well-made nonogram never needs a guess.
Below, each technique is shown on a real line. Every diagram on this page is checked by a solver when the site is built, so none of them can claim a square that isn't forced. We also measured how often each technique comes up on 3,000 puzzles from Poozee's Nonograms.
How nonogram clues work
Each number is the length of a block of filled squares in that row or column, in order from left to right (or top to bottom). Blocks are separated by at least one empty square. A 0 means the whole line is empty. Fill in every square the clues call for and a picture appears:
In the diagrams below, the blue squares and red Xs are the ones a technique has just proved. Everything else was already known.
How we measured
We made 1,000 puzzles of each size (5×5, 10×10 and 15×15) with the same generator the game uses, seeds 1 to 1,000. Then a program solved each one the way a careful person would: it tries the simplest technique on every row and column first, and only reaches for a harder one when nothing simpler works anywhere on the grid. We counted which technique proved each square and which puzzles needed each technique at least once. Our pictures are generated, not hand-drawn, so other puzzle books will differ in the details, but the techniques are the same everywhere.
1. Overlap (simple boxes)
Picture a block of 8 in a row of 10. Pushed all the way left, it covers squares 1 to 8. Pushed all the way right, it covers 3 to 10. Wherever it really sits, it covers squares 3 to 8:
With several blocks, use this shortcut. Add up the clue plus one gap between each pair of blocks, and subtract that from the line length. The result is the slack: how far any block can move. Every block longer than the slack has (length minus slack) squares that are always filled: the last ones of its leftmost position.
Overlap needs big numbers. A 2 1 in a row of 10 has a slack of 6, so it gives nothing yet. Scan for the biggest clues first, and for lines with a 0, which you can cross out completely. Applied to every row and column of a blank grid, overlap settled 61.9% of the squares on our 5×5 puzzles, 41.2% on 10×10 and 35.6% on 15×15.
2. Spaces: cross out what can't be filled
Crossing out empty squares is half the game. Three simple cases come up constantly:
- The line is finished. Once a line has all its filled squares, every other square is empty.
- A gap is too small. A stretch of open squares between Xs (or an X and the edge) that's shorter than the smallest block can't hold anything.
- The longest block is complete. A run as long as the biggest number in the clue can't grow, so it gets an X at each end.
Pro tip: Mark every empty square you're sure of. Xs are what make the next three techniques work, and a square you know is empty tells the crossing line just as much as a filled one.
3. Edge forcing
The edges of the grid are where blocks run out of room. A filled square near an edge has to belong to the first block in that direction, and an X near an edge can push the first block inward.
The second example is overlap again, on a shorter line: the Xs made the line two squares shorter, so the slack dropped from 4 to 2. Whenever an edge gets new Xs, count the slack again.
4. Joining and splitting
When two filled squares sit close together, ask which block each could belong to.
Joining: if both can only be part of the same block, fill the squares between them.
Splitting: if filling the square between them would make a block longer than any block in the clue, it has to stay empty.
5. Sliding blocks
Overlap works on middle blocks too, once Xs and filled squares limit how far they can slide. Slide the whole clue as far left as the marks allow, then as far right, and look for squares the same block covers both times.
Sliding also crosses out squares that no block can reach from any position. It's the most general of the techniques here, and on big puzzles it's often the only way forward late in the game.
6. Crossing lines
No row can be solved in isolation for long. The real rhythm of a nonogram is rows, then columns, then rows again: every square you settle in a row is a new fact for its column. Here's the heart from the top of the page, solved from a blank grid.
One more pass over the columns finishes the heart. On bigger grids you go back and forth many times. With complete line logic, counting one pass over every row plus one pass over every column as a round, our 5×5 puzzles took 1.9 rounds on average, 10×10 took 3.4, and 15×15 took 4.4 (and up to 14). A first pass over the rows alone settled only 22.7% of a 15×15.
How often you need each technique
Here's the share of all squares each technique proved when the program always used the simplest one available:
| Technique | 5×5 | 10×10 | 15×15 |
|---|---|---|---|
| Overlap | 61.9% | 41.2% | 35.6% |
| Spaces | 24.3% | 21.8% | 16.4% |
| Edge forcing | 13.8% | 35.0% | 35.4% |
| Joining and splitting | 0.0% | 0.6% | 5.4% |
| Sliding blocks | 0.0% | 1.3% | 7.2% |
And here's how many of the 1,000 puzzles of each size needed each technique at least once, meaning there was a moment when nothing simpler worked anywhere on the grid:
| Technique | 5×5 | 10×10 | 15×15 |
|---|---|---|---|
| Spaces | 986 | 1,000 | 1,000 |
| Edge forcing | 844 | 1,000 | 1,000 |
| Joining and splitting | 0 | 235 | 945 |
| Sliding blocks | 0 | 325 | 970 |
Overlap, spaces and edge forcing solve every 5×5 on their own, and 607 of the 1,000 10×10s. On a 15×15 you'll nearly always need joining, splitting and sliding too. Only 2 of the 3,000 puzzles ever needed anything beyond them: a step where the only way forward was to list every way a clue could fit its line and find a square they all agree on.
When you're stuck
- Re-check lines that just changed. A new X or filled square at the edge of a line often sets off edge forcing.
- Count the slack again on every line with new Xs near its ends.
- Name the owner of each filled square. For each one, ask which block it could be part of. When there's only one answer, join, split or cap it.
- Slide the whole clue left and right in your head and compare the two positions.
- Ask for a hint. In Poozee's Nonograms, Hint settles one square (filling it or crossing it out) and names the row or column that proves it and the technique it takes, so you see the reasoning, not just the answer.
Keep playing
- Play Nonograms: a daily 10×10 plus unlimited puzzles from 5×5 to 15×15
- Sudoku strategies, the same "what can fit here?" thinking with numbers
- Minesweeper patterns for another kind of logic grid
- Sudoku, with puzzles graded by the techniques they need
Frequently asked questions
Do you ever have to guess in a nonogram?
Not in a well-made one. Every puzzle on Poozee is checked by a solver that works one row or column at a time, so it can always be finished by logic alone. Puzzles from other sources sometimes need trial and error, or even have more than one answer.
Where should I start a nonogram?
With the biggest clues. A block longer than half its line always covers the middle squares, and a clue that nearly fills its line settles most of it. Rows and columns marked 0 can be crossed out completely.
Should I mark empty squares with an X?
Yes. Xs are what make spaces, edge forcing and splitting work. A square you know is empty is as useful as a filled one, because it tells the crossing line where its blocks can't go.
Are nonograms the same as Picross or Griddlers?
Yes, it's the same kind of puzzle under different names, along with Hanjie and Paint by Numbers. Picross is a Nintendo trademark.