Nonograms, and how Grandma’s Knitting knits them

What a nonogram is

A nonogram is a grid with numbers beside each row and above each column. You fill in squares. The rules:

• Each number is a run of filled squares in that row or column: a 3 means three filled squares side by side.
• The runs come in the order the numbers are written: left to right along a row, top to bottom down a column.
• Two runs in the same line have at least one empty square between them.
• When every row and column matches its numbers, the filled squares make a picture.

That last rule is the reward, but it’s also a warning: you can’t guess the picture and work back. A half-finished sail looks like a lot of things. You have to let the numbers draw it.

Where it came from

Nonograms come from Japan. In 1987 Non Ishida, a graphics editor, won a competition in Tokyo with a picture made from the lit windows of a skyscraper, and it gave her the idea for grid puzzles that make a picture. The professional puzzler Tetsuya Nishio invented the same puzzle on his own and published his in another magazine. In 1988 Ishida published three of hers as “Window Art Puzzles”.

James Dalgety, a British puzzle collector, named them nonograms, from Non and “diagram”, and from 1990 The Sunday Telegraph printed one every week. In 1998 its readers voted on a new name, and chose Griddlers. Hanjie, Paint by Numbers and Pic-a-Pix are other names you’ll see.

Nintendo calls them Picross, short for “picture crossword”. Mario’s Picross came out on the Game Boy in Japan in 1995, and the puzzle has been a Nintendo regular since: the Picross S series, made by Jupiter, has run on the Switch since 2017.

Big nonograms are hard in a precise sense: working out whether one has a solution at all is NP-complete, which roughly means no one knows a shortcut that settles every big one quickly. That’s why a good nonogram is made with care, and checked so it can be solved one line at a time.

How to solve a nonogram

Almost every step comes from one question about one line: where can its runs go, and what do all the ways agree on?

1. Start with the big numbers. A long run always covers the middle of its line. In a row of 8, a 6 covers the middle four squares wherever it sits. Solvers call this the overlap, or simple boxes.
2. Add a line up. Add the numbers, plus one for each gap. If that equals the line’s length, there’s only one way to fit it: 4 3 in a row of 8 is four filled, one empty, three filled.
3. Work from the edges. A filled square against the edge has to be the start of the first run, so the rest of that run follows, and the square after it is empty.
4. Finish what’s done. Once a line has all its runs, mark every other square in it empty. Each empty square gives the line crossing it less room.
5. Mark what no run can reach. If a row says 2 and its third square is filled, the 2 can only sit on squares two and three or three and four. Every other square in the row is empty.
6. Go back and forth. Every square you settle in a row is a new fact for its column, and the other way round. Sweep the rows, then the columns, then the rows again.

Hard nonograms add one more move: try a square both ways in your head and see which one breaks a line. A well-made puzzle never needs a pure guess.

Solving the sailboat, step by step

Here’s the little puzzle above, worked through. Its rows say, from the top: 1, 2, 3, 4, 1, 7, 5. Its columns say, from the left: 1, 2, 2, 7, 3 2, 2 2, 1 1.

1. The 7s. The grid is 7 squares across, so the sixth row’s 7 fills it, and the fourth column’s 7 fills that column from top to bottom.
2. The lines already done. The first column says 1, and it has its square in the sixth row: mark the rest of it empty. The first and fifth rows each say 1, and each has its square in the long column: mark the rest of them empty too.
3. The second column says 2. It has its square in the sixth row, and the fifth row is empty, so its run goes down: fill its bottom square.
4. The bottom row says 5. Its first square is empty and its second is filled, so its run is squares two to six, and the last square is empty. The third column now has its 2 in the bottom two rows: mark the rest of it empty.
5. The sail. The second, third and fourth rows each have a filled square in the long column, with an empty one just to its left. So each run starts at the long column and runs right: 2, 3 and 4 squares. Every line matches. It’s a sailboat.

How Grandma’s Knitting knits it

Grandma’s Knitting is our daily nonogram. Grandma is knitting a picture, and the numbers along her swatch say how. Knit every square right and the picture appears, in her own yarns.

What’s the same:

• Each number is a run of knitted squares in its row or column, in order, with at least one empty square between runs.
• A square is knitted or it isn’t. The yarns only show at the end, when the picture appears.
• Every picture has exactly one answer, and you can always reach it one row or column at a time. Each of Grandma’s pictures is drawn by hand and checked by a solver that knits it from the numbers alone, the way a player does. A picture it can’t finish is redrawn. (How we make puzzles with exactly one answer has more on how the family’s dailies are checked.)

What’s different:

• Always 8 across. Monday to Saturday the swatch is 8 × 8, and Sunday’s is 8 across and 10 tall, so the squares stay big enough to tap on a phone.
• One picture a day. A new one comes at midnight, your time, the same for everyone, with a par time and a streak.
• The picture hides again. Once it’s knitted, it shows for a moment and then the swatch goes plain, so a screenshot of your result doesn’t give the day’s picture away. “See your picture” brings it back.
• Lines fade when they’re right. A row or column whose squares match its numbers goes faint, so you can see what’s left.

Every habit above carries straight over. For a walk through the practice swatch, square by square, see our guide to nonograms. And if you like this kind of number logic, Hashi puzzles and Lacey’s Web is about another one.

Where to play nonograms

• Pattern, in Simon Tatham’s free puzzle collection, plays in a web browser. Its grids are made by a program, so they’re random patterns rather than pictures, and you can play as many as you like.
• Picross S is Jupiter’s series of Picross games for the Nintendo Switch, since 2017.
• Pic-a-Pix is Conceptis’s nonogram, in black and white and in color.
• Grandma’s Knitting is one new picture a day, free in your browser, about two minutes, with a streak and a time to beat.

Questions people ask