How to solve nonograms

Numbers along the edges describe runs of filled squares. Work out which squares they are, and a picture appears.

Each row and column carries a list of numbers giving the lengths of consecutive filled blocks, in order, with at least one gap between them. A clue of "4 2" means four filled, then a gap, then two filled.

Overlap: the technique to learn first

Consider a clue of 8 in a row of 10. Slide the block as far left as it goes, then as far right. The squares covered both times must be filled whatever happens — six of them here. You have made real progress without knowing the block's position at all.

This works whenever a clue is large relative to the space. It is the single most productive move in the game, and it applies to multi-block clues too, once you allocate minimum space to each.

Edges force things

If the first square of a row is filled, the first block starts there, so you can fill its whole length immediately and mark the square after it empty. Edges remove the ambiguity that overlap works around.

Mark the empties

Beginners fill squares and leave the rest blank. Marking squares you have proved empty is just as valuable, because it splits a row into shorter segments — and shorter segments make overlap bite harder. A row split into a length-3 and a length-4 region is far more constrained than an undivided row of 8.

Completion

When a row's filled squares already account for all its clue numbers, every remaining square in that row is empty. Sweeping for this after each deduction cascades usefully into the crossing columns.

Frequently asked questions

Do I need to guess?

No. Every puzzle is checked to have a unique solution reachable by deduction alone before it is offered.

What does a clue of 0 mean?

The row or column is entirely empty. It is worth filling in immediately, since it constrains every crossing line.

Why mark empty squares?

Because they split a line into shorter segments, and shorter segments make the overlap technique far more productive. Tracking only filled squares throws away half the information you have proved.