Nonogram

How to play

The numbers beside each row and above each column tell you the runs of filled squares in that line, in order, with at least one gap between runs. A row marked 3 1 has three filled squares, then a gap, then one more. Work out which squares must be filled and which must be empty, and the picture appears. Tap to fill, or switch to Mark mode to cross off squares you have proved are empty. Every puzzle here has exactly one solution, so you never need to guess.

Tips

• Start with the longest clues. A run of 8 in a 10 wide row leaves only three possible positions, and the middle squares are filled in all of them.
• Overlap is the core trick. Slide a run to its leftmost and rightmost positions, and any square covered both times must be filled.
• A line whose clues plus the gaps between them exactly fill its length is completely determined. Fill it immediately.
• Mark the empty squares, do not just leave them blank. Proven gaps carry as much information as filled squares.
• When a line stalls, switch to its crossing lines. Progress in a nonogram almost always comes from the other direction.

The puzzle that draws a picture

Nonograms were invented independently twice in the late 1980s, by a Japanese graphics editor named Non Ishida and a Japanese puzzler named Tetsuya Nishio, and the name comes from Ishida's surname. They spread through British newspapers in the 1990s as Griddlers and through Nintendo as Picross, and the format has not changed: numbers along the edges describe runs of filled cells, and solving the grid reveals an image.

The puzzles here are checked before you see them. A pattern is generated, its clues are derived, and a line solver then works through the clues by pure deduction. If deduction alone cannot finish the grid, the puzzle is thrown away and another is tried. That is the guarantee behind the promise that you never have to guess.

The core deductions

• Overlap: slide a run to its leftmost and rightmost positions. Any cell covered both times is filled. A run of 8 in a line of 10 fills the middle six immediately.
• Full line: if the clues plus the gaps between them exactly fill the length, the whole line is determined at once.
• Edge anchoring: a filled cell at the edge of a line must be the start of the first run, so you can extend it to that run's length and mark the cell after it empty.
• Marking empties matters. A cell you have proved blank constrains the crossing line as much as a filled one does.
• Switch axes when stuck. Progress almost always comes from the other direction.

Common questions

Can every puzzle be solved without guessing?

Yes. A puzzle is only kept if a line solver finishes it by deduction alone, so logic is always enough.

What does a clue like 3 1 mean?

Three filled cells, then at least one empty cell, then one filled cell, in that order along the line.

What is Mark mode for?

Crossing off cells you have proved are empty. Recording proven blanks is how the crossing lines get resolved.