Nonogram Rules: How to Play

The grid and the clues

Every cell of the grid is either filled or empty. Each row has a clue at its left and each column has a clue above it. A clue is a list of numbers.

Each number is the length of one group of filled cells in that line. The groups appear in the order of the numbers, from left to right in a row and from top to bottom in a column. Two groups are separated by at least one empty cell.

The clue does not say where a group starts, and it does not say how many empty cells lie between the groups or at the ends. Finding that out is the puzzle.

Reading a clue

The more room a clue leaves, the more arrangements fit. A clue whose numbers and gaps use up the whole line has one arrangement and can be filled in at once.

Filled cells, crosses and blanks

While you solve, a cell is in one of three states. Filled means you know it belongs to the picture. Crossed means you know it is empty. Blank means you do not know yet.

Crosses are as useful as fills. A crossed cell cuts a line into shorter pieces, and a group that does not fit into a piece cannot be there.

On this site the puzzle is solved when the filled cells form the picture. You do not have to cross every empty cell.

A complete example

A grid of 5 × 5 cells has these clues. Rows from top to bottom: 3, then 2 2, then 5, then 3, then 1. Columns from left to right: 2, then 4, then 1 3, then 4, then 2.

1. Row 3 has the clue 5 in a row of 5 cells: fill the whole row.
2. Row 2 has the clue 2 2. Two cells, a gap and two cells use all 5 cells: fill cells 1, 2, 4 and 5 and cross cell 3.
3. Column 1 has the clue 2 and already shows filled cells in rows 2 and 3. Its group is complete: cross rows 1, 4 and 5.
4. Column 5 has the clue 2 as well and is finished in the same way.
5. Row 1 has the clue 3. Its first and last cells are crossed, so the group lies in cells 2, 3 and 4. Row 4 has the clue 3 and the same crosses: fill cells 2, 3 and 4.
6. Row 5 has the clue 1, and its first and last cells are crossed. Column 2 has the clue 4 and already has four filled cells in rows 1 to 4, so its cell in row 5 is empty. Column 4 gives the same result. The single cell of row 5 is in column 3.

The finished picture, row by row:

Check column 3: it is filled in rows 1, 3, 4 and 5 and empty in row 2. That is a group of 1 and a group of 3, which matches its clue 1 3.

Every step used one row or one column. No cell was filled on a hunch.

Names and origin

The puzzle was invented in Japan in 1987, independently by Non Ishida and Tetsuya Nishio. It is also known as Hanjie, Picross, Griddlers and Paint by Numbers.

Deciding whether an arbitrary set of clues has a solution at all is a hard problem for computers: it has been proved to be NP-complete. Puzzles like the daily ones avoid this: they are built so that reasoning on one line at a time is enough.

• Nonogram solving techniques
• Play the daily nonogram

Common mistakes

• Reading a clue as positions. The clue 3 1 does not mean cells 3 and 1; it means a group of three and, later in the line, a group of one.
• Letting two groups touch. Groups of the same line always have at least one empty cell between them.
• Changing the order. The groups appear in the order of the clue and never swap places.
• Solving only rows. Every cell belongs to a row and a column, and progress comes from switching between them.