How to solve nonograms: rules and 5 techniques
A nonogram (also called Picross, Griddlers, Hanjie or paint by numbers) is a grid puzzle where number clues tell you which squares to fill. Solve it and a hidden picture appears. Every fair nonogram can be solved by logic, with no guessing.
The rules
Each row and column has a clue, a list of numbers. Each number is a run of filled squares in that line, in that order, with at least one empty square between runs. A clue of 3 1 means a run of three filled squares, then a gap of one or more, then a single filled square.
Mark squares you know are empty with a cross or dot. Empty squares are as useful as filled ones.
1. Start with the big clues
In a 10-wide row, a clue of 10 fills the whole row. A clue of 0 means the whole row is empty. Clues that add up to the full width (counting one gap between each run) are also solved at once: 4 5 in a 10-wide row is 4 filled, 1 empty, 5 filled.
2. The overlap trick
For a single big run, imagine it pushed as far left as it can go, then as far right. Squares covered in both positions must be filled. In a 10-wide row, a clue of 7 covers squares 1–7 when pushed left and 4–10 when pushed right, so squares 4 to 7 are certainly filled. Quick rule: if a run is longer than half the line, its middle is filled.
The same works with several runs: push all of them left, then all right, and look for squares where the same run lands both times.
3. Use the edges
If a filled square touches the edge of the grid, it must belong to the first run of that line. So a first clue of 3 with the edge square filled means the first three squares are filled and the fourth is empty.
4. Cross off what can’t be reached
Once a run is placed, squares too far from any remaining run can be crossed. If a row has clue 2 and you’ve found one filled square in the middle, every square more than one step away from it is empty.
5. Switch between rows and columns
Each new square you fill or cross gives the crossing line a new fact. Work a row, then check the columns it touched. Most puzzles are solved by going back and forth like this until the picture appears.
Like logic grids? Try the daily sudoku (and our sudoku guide) or Minesweeper with no guessing.