Nonograms (picross)

How it works

Before filling a single cell, understand that the number clues describe runs with at least one gap between them, and that the gaps are where the early certainty hides. A row clued 4 2 means a run of exactly four filled cells, then at least one empty cell, then a run of exactly two, somewhere along that line. The trick is that on tighter lines, the possible positions of those runs overlap, and the overlap is forced filled no matter where the runs ultimately sit.

Start with the most constrained lines, the ones whose clues nearly fill the row. In a 10-wide grid, a clue of 8 can only sit two ways, and the middle six cells are filled in both, so you can mark them immediately with certainty. Find every row and column where the numbers plus their mandatory gaps come close to the full width, and harvest the guaranteed cells first. These confirmed cells then give the crossing lines new constraints, and the solve spreads outward from there.

Mark empties as deliberately as fills, using a light dot or cross for cells you have proven cannot be filled. This is the half beginners neglect, and it is half the information. A crossed-out cell tells the perpendicular line that its run cannot extend there, which often forces a fill three cells away. Work fills and empties together, never guess in a properly made puzzle, and the hidden picture, a duck, a teapot, a tiny rocket, slowly emerges one forced deduction at a time.