Nonogram

The classic paint-by-numbers puzzle: get the edge numbers right and a hidden picture appears.

Size

The numbers tell you how many squares to fill in a row. Tap once to fill, twice for an X note.

What is a nonogram?

A nonogram is a picture logic puzzle that goes by many names: Picross, Griddlers, Hanjie, Japanese crosswords, or paint-by-numbers. You start with an empty grid. The numbers printed beside each row and above each column tell you exactly which squares to fill with ink. Solve them all and the grid turns into a little picture: a heart, a sailboat, a cat. Every square is worked out from the numbers, one at a time.

How to read the clues

Each number means a run of filled squares in a row: that many squares together, with no gaps inside the run. If a clue has two or more numbers, the runs appear in that order, and there is at least one blank square between them.

Here is a worked example. Imagine a row of five squares with the clue “1 3”. That means: one filled square, then a gap of at least one blank, then three filled squares together. Count it out: one filled, one blank, three filled makes exactly five. So the row can only be filled one way: fill the first square, leave the second blank, and fill the last three. Rows like this, where the clues use up the whole line, are the best places to start.

How to solve one

  • Start with the full lines. A clue of 5 on a five-square row (or 10 on a ten-square row) fills the whole line.
  • Use the big numbers. A 4 in a five-square row must cover the middle three squares no matter where it sits, so fill those first and come back for the ends.
  • Work the edges. Once a square touches the edge of a run, you often know exactly where the rest of the run goes.
  • Leave X notes. When you are sure a square stays blank, tap it twice to mark it with an X. The blanks are just as informative as the fills.
  • Watch the numbers dim. When a row or column is complete, its clue numbers fade and gain a small check mark border.

If you fill a wrong square, nothing happens: no flash and no penalty, as with a paper nonogram. Press Hint and one square is put right, with a note explaining what changed.

Similar puzzles

Cat Sudoku and Sudoku use the same square-by-square reasoning.

Where Nonogram came from

Nonograms, picture logic puzzles solved by using the number clues along each row and column to work out which squares to fill in, were developed in Japan in the late 1980s. The graphic designer Non Ishida is widely credited as one of the creators, publishing grid puzzles of this kind around that time, and the name nonogram is generally said to come from hers.

A similar idea was worked out separately by other puzzle designers around the same period, which happens fairly often with logic puzzles simple enough in their basic rule that more than one person can arrive at them. The puzzles later spread beyond Japan under several names, including picross and griddler, before nonogram became a common term for them. Solving one here works the way it always has: read the clues on the edge, and no guessing is needed. Try more in my brain puzzles.