Nonograms for Beginners: How to Solve Picture Logic Puzzles
Learn to read nonogram clues and use the overlap and edge techniques that solve most small and medium picture puzzles.
Nonograms are logic puzzles that reveal a picture when you solve them. They go by many names, including Griddlers and Paint by Numbers. You fill in squares on a grid using number clues for each row and column. No guessing is needed in a well-made puzzle, and the hidden picture at the end is a nice reward.
How to read the clues
Each row and each column has a list of numbers. Each number is a run (also called a block) of consecutive filled squares.
- A row clue of 3 1 means: somewhere in this row there is a run of 3 filled squares, then at least one empty square, then a run of 1.
- The runs appear in the order listed, from left to right for rows and top to bottom for columns.
- Between two runs there must be at least one empty square. There can be more.
- A clue of 0 (or an empty clue) means the whole line is empty.
Most players mark squares they know are filled with a solid color, and squares they know are empty with an X or dot. Marking empties is just as important as filling squares.
Technique 1: Full lines
If the clues plus the minimum gaps add up exactly to the line length, the line is completely determined.
Example: a row of length 10 with clue 4 5. The runs need 4 + 5 = 9 squares, plus 1 gap = 10. So the row is: four filled, one empty, five filled. Fill it right away.
Technique 2: Overlap (the most useful technique)
When a run is long compared to the line, it must cover certain squares no matter where it sits.
Example: a row of length 10 with a single clue 7. If you push the run as far left as possible, it covers squares 1 to 7. Push it as far right as possible, and it covers squares 4 to 10. The squares covered in both positions, 4 to 7, must be filled.
This works with multiple runs too. Push all runs as far left as they can go, then as far right, and fill any square where the same run covers it in both positions.
A quick rule of thumb for a single run: if the run length is more than half the line length, there is an overlap to fill.
Technique 3: Edges and anchors
When a filled square touches the edge of the grid, the run that includes it must start at that edge.
Example: a row with clue 3 ... and the first square is filled. That filled square must belong to the first run, which must be squares 1 to 3. Fill them and mark square 4 as empty.
Technique 4: Completed runs
Once a run is complete, mark the squares on both sides of it as empty. Also, once all runs in a line are placed, mark every remaining square in that line as empty. These X marks feed into the crossing lines and create new deductions.
Technique 5: Working back and forth
Nonograms are solved by alternating between rows and columns. Every square you fill or mark in a row gives new information to the column it sits in, and the other way round. When you get stuck, scan every row and column again with fresh eyes.
A good solving routine
- Start with full lines and lines with large clues.
- Apply overlap to every line where a run is longer than half the space available.
- Mark empties next to completed runs.
- Switch between rows and columns, applying the same techniques.
- Check the edges for anchored runs.
Choosing your first puzzles
Start with 5×5 or 10×10 puzzles. Larger grids such as 15×15 or 20×20 use the same techniques but require more bookkeeping. Once you can solve 10×10 puzzles without hints, move up gradually.
Nonograms reward patience and careful marking. Mark empties generously, and the picture will appear one line at a time.