How to read the clues, and the line-by-line logic that fills a grid without guessing
A nonogram is a grid puzzle in which numbers beside each row and above each column describe the runs of filled cells in that line. From those clues alone, you work out exactly which cells are filled. The puzzles go by many names, including Picross, Griddlers, Hanjie and Paint by Numbers. They originated in Japan in the late 1980s, where Non Ishida and Tetsuya Nishio both came up with the idea independently around 1987 and 1988. The name "nonogram" combines Ishida's first name with "diagram". The puzzles reached a wide Western audience through the British newspaper The Sunday Telegraph from 1990, and later through Nintendo's Mario's Picross in 1995.
Traditional nonograms are hand-designed so that the filled cells form a picture. Ours are different: each puzzle is a freshly generated random pattern with roughly 55% of the cells filled. There is no image to guess at, so every cell has to be earned by logic. The high density also means lines are crowded, which makes the overlap techniques below especially productive.
Every technique starts with one number. Add up a line's clues, add one for each gap between runs, and subtract the total from the line length. The result is the slack, which tells you how far the runs can shift. For "3 4" in a 10-cell row, the minimum length is 3 + 1 + 4 = 8, so the slack is 2. A line with zero slack is completely determined. "2 2" in a 5-cell row must be filled, filled, empty, filled, filled.
Slide every run as far left as it can go, then as far right. Any cell covered in both positions must be filled. The shortcut: each run longer than the slack fills (run length − slack) cells. A single 7 in a 10-cell row has slack 3, so it fills 7 − 3 = 4 cells: positions 4 to 7. For "3 4" (slack 2), the leftmost placement puts the 3 on cells 1–3 and the 4 on 5–8. The rightmost puts the 3 on 3–5 and the 4 on 7–10. Cell 3 and cells 7–8 are certain. A run no longer than the slack gives nothing yet.
The reverse also works: a cell that no run can reach must be empty. If a 10-cell row has the clue "3" and you already know cell 5 is filled, the run must cover cell 5, so it lies somewhere within cells 3–7. Cells 1–2 and 8–10 are empty.
Walls are powerful. If the first cell of a row is filled and the first clue is 4, that run must start at the wall: fill cells 1–4 and mark cell 5 empty. If cell 2 is filled and the first clue is 3, the run contains cell 2 and starts at cell 1 or 2, so cell 3 is filled too. Empty cells act like walls. If cell 3 is known to be empty and the first clue is 3, cells 1–2 can't hold that run, so they're empty and the run starts at cell 4 or later.
Compare what you have with what the clue demands. When the filled cells in a line already account for every run, everything else is empty. A gap between two empty cells that is too short for any remaining run must stay empty: two free cells can't hold a 3. Use run sizes to tell runs apart. In a row clued "1 4", any filled stretch of two or more cells must belong to the 4, which pins down where the 1 can go.
Sweep every row for overlaps and zero-slack lines, then every column, then return to the rows. Each settled cell is a new fact for the line crossing it, and following those knock-on effects is how a grid unravels. On a 15×15, where slack is large, progress comes from steady back-and-forth rather than a single breakthrough.
Because our puzzles are random and not checked for a unique solution, occasionally two different patterns fit every clue. The classic case is a rectangle of four cells where the filled pair could sit on either diagonal without changing any run. This happens most often on the 15×15. Make sure you have truly exhausted every line first, because the deduction you need is usually in a crossing line you haven't revisited.
Since every click is a move, a perfect score is one click per filled cell. With about 55% of cells filled, that averages roughly 14 moves on a 5×5, 55 on a 10×10 and 124 on a 15×15. Each wrong fill costs two moves (one to place and one to clear), and each X adds one, so keep track of proven empty cells in your head where you can. Save X marks for spots where they genuinely prevent a mistake.
Difficulty is the grid size. The fill density, controls and scoring are the same at every level.
| Difficulty | What changes |
|---|---|
| Easy | 5×5. Lines are short and slack is small, so many lines are fully determined straight away. It's ideal for learning overlap and edge logic. A perfect solve averages about 14 moves. |
| Medium | 10×10, the size the page opens with. Clues often run to three or four numbers, and you'll need regular row-and-column cross-referencing. About 55 filled cells on average. |
| Hard | 15×15. Lines have much more slack, single clues settle fewer cells, and the odds of a spot where more than one pattern fits are highest. About 124 filled cells on average. |
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