To make a nonogram, draw a picture on grid paper, count the runs of filled squares in every row and column to get the clues, then solve your own clues from a blank grid, one row or column at a time, without looking at the picture. If you can finish that way, the puzzle has exactly one solution and never needs a guess. If you get stuck, the squares you couldn't settle show where the problem is, and changing just one square nearly always fixes it.
The steps below walk through a real design, from a first draft that has two solutions to the one-square fix. We tested the advice with code on 18,000 random pictures, and every diagram on this page is checked by a solver when the site is built.
What makes a good nonogram
A good nonogram passes two tests:
- It has exactly one solution. If two pictures fit the same clues, a solver can finish "correctly" and still not get your picture.
- It can be solved by logic alone. Every square can be proved from what one row or column says, using the techniques in how to solve nonograms. Nobody should have to guess and check.
The second test is the one to aim for, because it includes the first: if pure line-by-line logic fills the whole grid, no other picture can fit. A puzzle can pass the first test and still fail the second. This little face has exactly one solution, but line logic stalls with eight squares open, and the only way on is trial and error:
Step 1: Pick a size and draw the picture
Start small. A 5×5 is perfect for young kids or a first try, and a 10×10 is enough for a real picture: a fruit, an animal's face, a boat, a house. Draw it on grid paper in pencil, or in a spreadsheet with filled cells.
Three things make a picture much more likely to work:
- Fill more than half the squares. Solid shapes beat outlines. In our tests, about 60% filled was the sweet spot (the numbers are below).
- Draw diagonals as stair steps. Squares that touch only at their corners are a common cause of a second solution. Make each square of a diagonal line share an edge with the next one.
- Avoid lone specks. A single square floating on its own, with a lot of empty space around it, can usually slide somewhere else.
Step 2: Write the clues
For each row, read left to right and write the length of each run of filled squares, in order. Do the same for each column, top to bottom. A row or column with nothing filled gets a 0.
Check every clue twice. One miscounted run makes the puzzle impossible, and it's the easiest mistake to make on a big grid.
Step 3: Solve your own clues from a blank grid
Copy just the clues onto a fresh grid, put your drawing away, and solve. Only mark a square when one row or column proves it: overlap, crossing out, edge forcing and the other techniques in our solving guide. Keep switching between rows and columns until nothing changes.
If you fill every square, you're done: the puzzle has one solution and can be solved without guessing. If you get stuck, don't guess. The open squares are your clue to what's wrong.
Here's a first draft of a pair of cherries. Line logic settles 96 of the 100 squares, then stops:
Step 4: Find the second solution
Look at the open squares: they form a 2×2 block in rows 3 and 4, columns 5 and 6. In the drawing, the stem's squares in that block touch only at their corners. Swap them to the other diagonal and every row and column still has the same clue, so both of these pictures fit:
A solver that searched every possibility found exactly these two, and nothing else. When you get stuck on your own puzzle, try the same thing: look for squares in the open area that could trade places, two filled and two empty at the corners of a rectangle.
Step 5: Fix it with one square
To break the tie, change one square so the two diagonals no longer match. Filling one of the empty corners is usually the best choice, because it keeps the picture's shape. Here, filling row 4, column 6 turns the stem into a stair step:
The changed square altered two clues: row 4 is now 2 1 and column 6 is 2. Always rewrite the clues after an edit, and solve again from a blank grid.
We tried all 100 possible one-square changes on the draft: 12 of them make it solvable by line logic, and all 4 squares of the checkerboard are among them. Two of those four erase part of the stem, though, so filling is the better fix.
The classic mistakes
Squares that touch only at their corners
Two filled squares on a diagonal, with the other two squares of their 2×2 block empty, can often swap to the other diagonal without changing a clue. That's what happened to the cherries. Diagonal lines drawn one square at a time are full of these.
Pieces that slide in opposite directions
The swapping squares don't have to be neighbors. Any four squares at the corners of a rectangle can trade places when the clues allow it. In this boat, the sail's bottom row and the hull's bottom row can both slide one square, in opposite directions:
The fix is the same: change one corner. Erasing row 3, column 5 makes the sail 1, 2, 2 squares wide, and line logic then solves it.
Too few filled squares
Outlines, thin lines and rows with just one or two filled squares give the solver very little to work with: a lone 1 in a row of 10 could be in any of 10 places. Sparse pictures failed far more often than full ones in our tests.
What the numbers say
We drew random pictures with Poozee's seeded random number generator (seeds 1 to 1,000 for each size and density), filling every square with the same chance, and checked each one twice: with line logic from a blank grid, and with a complete search for a second solution. Random noise isn't a drawing, but it shows clearly which choices help.
Share of random pictures that line logic solved completely (so they had one solution and needed no guessing):
| Filled | 5×5 | 10×10 | 15×15 |
|---|---|---|---|
| 30% | 39.8% | 0.9% | 0.0% |
| 40% | 53.9% | 12.1% | 1.3% |
| 50% | 73.8% | 52.6% | 26.5% |
| 60% | 88.6% | 83.7% | 74.6% |
| 70% | 95.6% | 96.1% | 95.4% |
| 80% | 99.2% | 98.9% | 99.8% |
Pictures with one solution that still needed a guess, like the face above, were rare: 214 of the 18,000.
Why 60% is the sweet spot. Fuller pictures almost always work, but they give themselves away. On the 10×10s that worked, the very first overlap pass settled 47.8% of the squares at 60% filled, 69.9% at 70% and 87.9% at 80%. At 80%, 93.1% of them could be finished with just the three simplest techniques (overlap, crossing out and edge forcing), against 29.2% at 60%.
Swapping corners explains most second solutions. Of the 6,858 pictures with more than one solution, 93.3% had four squares at the corners of a rectangle that could trade places, and 37.6% had a 2×2 checkerboard that could.
One square usually fixes it. We took the 163 random 10×10 pictures at 60% filled that line logic couldn't finish and tried changing every square, one at a time. A single change made 150 of them solvable. Where you change it matters:
- A square line logic had left open fixed the puzzle 57.9% of the time; a square anywhere else, 6.4%. On average, only 6.5 squares were left open.
- Filling an empty square fixed it 16.7% of the time, erasing a filled one 4.5%.
Clean shapes help. Poozee's Nonograms makes its puzzles the same way: it draws random pictures and keeps only the ones line logic solves completely. A 5×5 is drawn 60% filled; a 10×10 or 15×15 is drawn 55% filled, then a smoothing pass fills lone holes and clears lone specks. With those settings it keeps 88.6% of 5×5 drawings, 75.3% of 10×10s and 58.6% of 15×15s. Without the smoothing pass, the same drawings give 71.5% and 55.3%.
Pro tip: If a puzzle won't come out, don't redraw it. Solve it until you're stuck, then change one of the squares you couldn't settle (filling beats erasing), rewrite the clues and solve again.
Keep playing
- Play Nonograms: a daily 10×10 plus unlimited 5×5, 10×10 and 15×15 puzzles, each checked by line logic before you see it
- How to solve nonograms: the techniques you need to check your own puzzle, with worked examples
- How to make a word search: the same idea for a word puzzle, from grid size to the checks that catch accidental extra words
- Minesweeper 50/50s: the same "logic or a guess?" question on a different grid
- Sudoku strategies, for another puzzle where a good one has exactly one answer
Frequently asked questions
Can a nonogram have more than one solution?
Yes. Clues only count blocks of filled squares, so two different pictures can share every clue. The usual cause is four squares at the corners of a rectangle that can trade places, such as two squares touching only at their corners.
How do I check that my nonogram has only one solution?
Copy the clues onto a blank grid and solve them without looking at your picture, settling only squares that a single row or column proves. If you can fill the whole grid that way, there's exactly one solution and nobody will ever need to guess.
What size should my first nonogram be?
5×5 for young kids or a first try, 10×10 for a real puzzle. A 15×15 takes much longer to check by hand, and in our tests random 15×15 pictures failed more often than smaller ones at every density up to 70% filled.
How do I make a nonogram easier or harder?
Fill more squares to make it easier: big clues give a lot away at the start. Fewer filled squares make it harder, but also make a second solution more likely, so check it again after every change.
Is a nonogram the same as a Picross puzzle?
It's the same kind of puzzle, also called Griddlers, Hanjie or Paint by Numbers. Picross is a Nintendo trademark, and the method here works for any of them.