# How to Solve Nonograms (Picross): Rules and Strategies Source: https://silverapuzzles.com/guides/how-to-solve-nonograms A nonogram is solved one line at a time. Each number beside a row or above a column is the length of a run of shaded cells, in order, with at least one empty cell between runs. Find the cells that must be shaded in every possible arrangement of a line, shade them, and let the crossing lines take it from there. ## What the numbers mean A clue of **3 1** on a row means: somewhere in this row there is a run of three shaded cells, then at least one empty cell, then a single shaded cell, in that order from left to right. A clue of **0** means the whole line is empty. When every line matches its clue, the shaded cells form a picture. *Figure: One arrangement that satisfies the clue 3 1 on a line of ten cells.* Nonograms are also sold as Picross, Griddlers, Hanjie and Paint by Numbers. They were first published in Japan in 1987. ## The overlap method The single most useful technique: imagine the run pushed as far left as it can go, then as far right as it can go. Any cells covered in *both* positions must be shaded. *Figure: A run of 8 in a line of 10: pushed left it covers cells 1–8, pushed right it covers cells 3–10. Cells 3–8 are shaded in both, so they must be shaded.* The rule of thumb: if a run of length *k* sits in a line of length *n*, and *k* is more than half of *n*, then 2*k* − *n* cells in the middle are certain. With several runs, add them up with one gap between each, and apply the same push-left, push-right idea to every run. ## Edges and finished lines Once a shaded cell touches an edge, the run it belongs to must start there. If the first clue in a row is 4 and the first cell is shaded, the first four cells are shaded and the fifth is empty. When a line already matches its clue, mark every remaining cell as empty with an × (in our game, switch to Cross or right-click). Those crosses are information for the crossing lines. *Figure: The shaded edge cell anchors the run of 4. Every other cell in the line must be empty.* ## Gaps, splitting and counting Crossed-out cells split a line into segments. A segment that is shorter than the smallest run still to be placed can never hold a run, so cross it out too. When a line has two runs and a shaded cell sits between their possible ranges, ask which run it can belong to; often only one fits, which fixes that run’s position. Counting helps on big grids. The total of a line’s clues plus one gap between each run gives the minimum space the line needs. If a row of 15 cells has the clue 4 5 3, the runs need 4 + 5 + 3 + 2 = 14 cells, leaving only one cell of slack. Push every run left, then right: almost every cell is decided at once. ## A worked example: a 5×5 heart Our smallest nonogram is a heart. The row clues from top to bottom are **1 1**, **5**, **5**, **3**, **1**, and the column clues from left to right are **2**, **4**, **4**, **4**, **2**. 1. Rows 2 and 3 have a clue of 5 in a line of 5, so every cell in both rows is shaded. 2. Columns 2, 3 and 4 have a clue of 4. Each already has rows 2 and 3 shaded; the overlap method shades rows 2–4 of each of these columns. 3. Row 4 now has its three middle cells shaded, matching the clue 3, so its first and last cells are crossed out. 4. Columns 1 and 5 have a clue of 2 and already contain rows 2 and 3, so rows 1, 4 and 5 of those columns are empty. 5. Row 1 needs 1 1 with its outer cells empty: the only arrangement left is columns 2 and 4. Row 5’s single cell must be in column 3, the only column whose run of 4 can still reach that far. Five lines of reasoning and the heart appears, without a single guess. ## Mistakes to avoid - **Shading from a hunch.** Only shade a cell when every possible arrangement of the line shades it. - **Ignoring crosses.** Empty cells carry as much information as shaded ones. Mark them. - **Reading clues out of order.** Runs appear in the order given: a clue of 1 3 means the single cell comes before the run of three. ## A routine for every puzzle 1. Start with the biggest clues: the lines where the runs nearly fill the line. Apply the overlap method. 2. Switch to the crossing direction. Every new shaded cell or × gives you a fresh constraint. 3. Complete lines whose clue is satisfied by crossing out the rest. 4. Use edges and gaps: a gap of empty cells too small for any remaining run must be crossed out. 5. Repeat until the picture appears. Every nonogram on our site is checked by a line solver, so this routine always finishes it without guessing. Practice: [play a nonogram](https://silverapuzzles.com/nonogram). ## Frequently asked questions **What does a 0 clue mean in a nonogram?** The line has no shaded cells at all. Cross out every cell in it. **Do I ever need to guess in a nonogram?** Not in a well-made one. Every nonogram on Silvera PuzzleClub is checked so that it can be finished by reasoning about one row or column at a time. **Is Picross the same as a nonogram?** Yes. Picross, Griddlers, Hanjie and Paint by Numbers are all names for the same kind of picture logic puzzle.