What is a nonogram?

Each number is the length of one unbroken run of filled squares in that line, and the numbers are given in the order those runs appear. Runs are separated by at least one empty square. Everything else about their position is for you to work out.

A row of ten squares clued 7 holds one run of seven somewhere. It can start at the first square or as late as the fourth, which sounds like four possibilities and no progress. It is not: push the run as far left as it can go, then as far right, and the squares covered both times must be filled.

That single idea, applied line after line, solves most of a puzzle. The step-by-step guide works through the rest of the techniques.

The puzzle collects names the way few others do, and they all describe the same thing.

• Nonogram is the usual name in puzzle books and the one these books use.
• Picross comes from Nintendo's handheld series and is what most video-game players call it.
• Hanjie is the common name in British newspapers and magazines.
• Griddler is used by several puzzle publishers and websites.
• Paint by numbers and pic-a-pix turn up in collections and apps.

If you learned the puzzle as any of those, you already know how to use these books. Nothing about the rules changes with the name.

A nonogram is only worth solving if its clues admit a single answer. When two different fillings satisfy the same clues, the puzzle cannot be reasoned to the end, and at some point you have to pick one and hope. That is the difference between a puzzle and a chore, and it is not visible from the outside: an ambiguous puzzle looks exactly like a sound one until you are twenty minutes in.

Every grid in these books was checked by a solver before it was printed, confirming both that the answer is unique and that deduction alone reaches it. It is why a contradiction you find while solving is always real information rather than a fault in the puzzle.

The reward for finishing is the image the filled squares make. Ours are symmetrical geometric patterns in the easy, medium and hard volumes, and recognizable seasonal pictures in the Halloween one. The grid below is a finished 10 by 10, solved in three passes on the how-to page.