Nonogram

A nonogram is a grid puzzle where the numbers around the edges tell you how the squares are filled. Each number is a run of consecutive filled squares, listed in order, separated by at least one gap. Solve every row and column and a picture emerges.

Also known as Picross, griddlers, or paint-by-numbers.

How to play

1. Read a row’s clues — 4 2 means four filled squares, at least one gap, then two filled.
2. Click a square to fill it. Right-click, or switch on mark mode, to cross off a square you know is empty.
3. Use the crossing clues to narrow each line down.
4. When every row and column matches its numbers, the picture is complete.

The opening move: overlap

On a large clue you can fill squares before deducing anything at all.

Take a clue of 7 in a ten-wide row. Pushed as far left as it goes, it covers squares 1–7. Pushed as far right, it covers 4–10. Squares 4, 5, 6 and 7 are covered either way, so they are filled — guaranteed, with no other information.

This works on any clue longer than half the line, and on combinations of clues that nearly fill a line. It is how every large nonogram opens, and skipping it is why beginners stare at an empty grid.

Crossing off is half the game

Filled squares get all the attention, but the crosses do just as much work. A crossed square splits a line into shorter segments, and short segments have far fewer arrangements. Players who only fill squares end up stuck on boards that are actually solved; players who mark empties as diligently as fills tend not to get stuck at all.

Why any consistent grid wins

The win condition here checks your grid against the clues, not against the picture the generator started from. That is the mathematically correct rule: if your filled squares satisfy every row and column, you have solved the puzzle, whatever the generator happened to have in mind.

Tips

• Start with the longest clues. In a ten-wide row, a clue of 8 has only three possible positions and the squares common to all of them are certain — that overlap is free information before you deduce anything.
• Cross squares off as aggressively as you fill them. Known-empty squares constrain the crossing lines just as much as filled ones, and most people under-use them.
• Whenever you fill a square, immediately re-read the crossing line. Nonograms are solved by bouncing between rows and columns, not by finishing one line at a time.
• A row whose clues plus the gaps between them equal the row width is completely determined. Look for these first; there is usually at least one on any board.