How to Solve Nonograms: A Beginner's Guide
To solve a nonogram, work one row or column at a time and only mark squares you can prove. Start with lines whose clues add up to the whole line, then use the overlap: slide each block as far left and as far right as it goes, and fill the squares it covers both times. Cross out squares no block can reach, then switch between rows and columns until the picture appears.
How nonogram clues work
A nonogram is a grid with numbers beside each row and above each column. Each number is a block of filled squares in that line, in order. "3 1" means a block of 3, then at least one empty square, then a block of 1. A 0 means the whole line is empty. Fill every line so it matches its clue and a pixel picture appears.
The puzzles were invented in Japan in the late 1980s, by Non Ishida and, independently, by puzzle maker Tetsuya Nishio. The name nonogram comes from "Non" plus "diagram", and you'll also see them called griddlers, hanjie, paint by numbers or picross.
Technique 1: Lines that add up exactly
Add up the clue numbers, plus one gap between each pair of blocks. If the total equals the length of the line, there's only one way to fit it, and you can fill the whole line at once. A clue that equals the line length (like a 5 in a row of 5) is the simplest case.
Technique 2: The overlap (simple boxes)
This is the most useful trick in nonograms. Push a block as far as it can go to one end, then as far as it can go to the other. Any square covered both times must be filled, wherever the block really is.
A quick way to count it: the overlap is the clue minus the empty space left over. Here 10 − 7 = 3 spare squares, so 7 − 3 = 4 squares are certain. Any block bigger than half its line gives you something on an empty line.
It works with several blocks too. Pack them all to the left with one gap between each, then all to the right, and compare each block with itself:
Only compare a block with itself. Where the 3 pushed right overlaps the 4 pushed left, nothing is proven, because those are different blocks.
Technique 3: Cross out squares no block can reach
Once a line has some filled squares, the blocks can't slide as freely. Work out how far each block can still reach; any square outside every block's reach must be empty, so cross it out (this is sometimes called simple spaces).
Technique 4: Forcing from the edge
A filled square on the edge of the grid (or right next to a crossed-out square) can only be the start of the first block. So the whole block is fixed, and the square after it must be empty.
A filled square near the edge works in a similar way. In a row whose first clue is 3, a filled second square means the 3 must also cover the third square, because the block can't start any further left than the edge.
Technique 5: Finished blocks and finished lines
- A complete block gets a cross on each side. If a block is already as long as its clue, the squares just before and after it must be empty.
- A finished line gets crossed out. When all of a line's blocks are drawn, every other square in it is empty. On GameLake, switch on Auto ✕ and the game crosses them for you.
- A 0 clears the whole line. Cross out every square.
Crosses matter as much as fills. Every cross shortens the space a block can slide in, which feeds straight back into the overlap and reach techniques for the lines that cross it.
Putting it together: solve a 5×5 heart
Here is the heart from the top, solved with nothing but the techniques above, switching between rows and columns:
Solving nonograms on GameLake
Every GameLake nonogram has been checked by a solver to have a single answer you can reach one line at a time, using only the kind of reasoning in this guide, so you never need to guess. Pick Easy (5×5 to 8×8), Medium (10×10), Hard (15×15) or the Daily picture, which is a 10×10.
- Tap a square to fill it, or drag along a line to fill several. Switch to ✕, or press and hold, to cross squares out.
- Easy, Medium and the Daily show a wrong square straight away; Medium and the Daily give you three lives. Hard checks nothing until the picture is right, so use crosses to keep track.
- Stuck? Teach me highlights the next squares you can work out and says why, in the same terms as above: a line that adds up exactly, the overlap (for a 7 in a row of 10: "wherever it starts, the middle 4 must be filled"), squares no block can reach, a block that can only go in one place, or a finished line to cross out.
Frequently asked questions
How do you solve a nonogram?
Work one line at a time. Fill lines whose clues add up to the full length, use the overlap trick on big clues, cross out squares no block can reach, and keep switching between rows and columns.
Where should I start a nonogram?
With the biggest clues and the lines that add up exactly, such as a 5 in a row of 5 or 4 5 in a row of 10. They give you squares on an empty grid.
Do you have to guess in nonograms?
Not in a well-made puzzle. Every GameLake nonogram can be solved by logic one line at a time, with a single answer.
What does a 0 mean in a nonogram?
That line has no filled squares at all, so you can cross out every square in it.
What are nonograms also called?
Griddlers, hanjie, paint by numbers and picross are other names for the same kind of picture logic puzzle.
Who invented nonograms?
Non Ishida and Tetsuya Nishio, independently, in Japan in the late 1980s. The name comes from "Non" and "diagram".