How to solve Nonograms: line by line to the picture
6 min read ·
A Nonogram hides a picture in a grid. The numbers beside each row and above each column give the lengths of the filled runs in that line, in order. Fill the right cells and the picture appears.
Every Nonogram on Puzzimo can be solved one line at a time, without guessing. This guide shows the handful of line techniques that do all the work.
The rules
- Each clue number is a run of consecutive filled cells in that row or column.
- The runs appear in the order of the clue, left to right or top to bottom.
- Between two runs there's at least one empty cell.
- Mark cells you know are empty with ✕: they're as useful as filled ones.
The overlap method
Take a single big run in a line. Slide it as far left as it can go, then as far right. The cells it covers in both positions must be filled, wherever the run really is.
In a row 10 cells wide, a run of 7 covers cells 1 to 7 when pushed left and 4 to 10 when pushed right, so cells 4 to 7 are certainly filled. The rule of thumb: a run of length k in a line of width w fills its middle 2k − w cells, whenever 2k is more than w.
Lines that fill completely
Add up a line's runs plus one gap between each pair. If the total equals the width, there's only one arrangement. In a 10-wide row, the clue 4 5 (4 + 1 + 5 = 10) fills the row exactly. A clue of 0 means the whole line is empty: ✕ it all.
Working from the edges
A filled cell next to the edge of the grid belongs to the first run of that line. That run must start there, so you can fill the rest of it and put a ✕ just after it.
- A filled cell at the very start of a line with clue 3 2 means cells 1 to 3 are filled and cell 4 is empty.
- An ✕ near the edge works too: if the first run can't fit before it, the run starts after the ✕.
- Gaps that are too small for any run left to place go ✕.
Cross-check rows and columns
Every cell you fill or ✕ in a row is new information for its column. The steady rhythm of a Nonogram is: work all the rows, then all the columns, then the rows again, each time with a few more cells known. On bigger grids, keep an eye on lines that just received a new cell; they're the ones most likely to move forward.
A solving routine
- ✕ every line with a clue of 0 and fill every line whose clue fills it exactly.
- Apply the overlap method to every line with a big run.
- Work from the edges: complete runs that touch the border.
- ✕ cells that no run can reach and gaps too small for the remaining runs.
- Alternate between rows and columns until the picture is complete.
Practise
Puzzimo's Nonograms come in 5×5, 10×10 and 15×15; the daily challenge is 10×10. Tap or drag to fill, and switch to ✕ with the toggle (or the X key). A fill on a cell that should be empty, or a ✕ on one that should be filled, counts as a mistake: the cell flashes and is corrected, and the third mistake ends the round.
Frequently asked questions
What is the overlap method in Nonograms?
Place a run as far as it can go in one direction, then as far in the other. The cells it covers in both positions must be filled. It's the main way to start any line with a big clue.
Are Nonograms the same as Picross and Griddlers?
Yes. Nonogram, Picross, Griddlers, Hanjie and paint-by-numbers puzzles all use the same rules.
Should I mark empty cells?
Yes. ✕ marks are half of the logic: they show where runs can't go, which tells you where they must go. Puzzimo counts a wrong ✕ as a mistake too, so mark only what you're sure of.