Pastime Arcade

How to Solve Nonograms

Every square can be worked out from the clues. These are the moves that do it, each shown on a diagram, then a whole puzzle solved from start to finish.

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Tap or click a square to fill it; drag to fill a line. Right-click, or switch to Cross, to mark a square you know is empty. Every puzzle can be solved by logic alone, with one answer. Keys: arrows move, Space fills, X crosses.

What the clues mean

Each number in a clue is a block of filled squares. The blocks come in the order the numbers are written, from left to right in a row and from top to bottom in a column, with at least one empty square between them. Before and after the blocks there can be any number of empty squares.

3 1 2
The clue 3 1 2: a block of three, then one, then two. This is one arrangement that fits; on its own the clue does not say where the blocks go.

Solving is a matter of finding squares that are filled, or empty, in every arrangement that fits the clue and what you already know. You only ever mark those. Every technique below is a quick way to spot them.

1. The overlap: big blocks cover the middle

Push the block as far left as it can go, then as far right. The squares it covers both times are filled whichever way it really sits.

7Pushed to the left
7Pushed to the right
7Filled in both
A block of 7 in a row of 10: squares 4 to 7 are filled in both positions, so they are certainly filled.

A quick rule: a block of length b in a line of length n fills the middle 2b − n squares when b is more than half of n. The same works with several blocks: pack them all to the left, then all to the right, and compare each block with itself.

4 3Pushed to the left
4 3Pushed to the right
4 3Filled in both
The clue 4 3 in a row of 10. The 4 covers squares 3 and 4 in both positions and the 3 covers square 8.

2. When the clue fills the whole line

Add up the blocks and one gap between each pair. If that equals the length of the line, there is only one arrangement.

3 3 2Before
3 3 2After
3 + 1 + 3 + 1 + 2 = 10, the whole row, so every square is decided.

3. Starting from a filled square near an edge

A filled square close to the edge limits where its block can be. If the first block must include that square, it cannot start further right than the square itself, and it cannot reach further than its length allows.

4Before
4After
The clue is 4 and square 2 is filled. The block must start at square 1 or 2, so squares 3 and 4 are filled too, and squares 6 to 10 are out of reach.

4. Gaps that are too small

Crosses split a line into separate gaps. A gap shorter than the smallest block that could go there must stay empty, and if only one gap is long enough, the overlap rule works inside it.

3Before
3After
The clue is 3. The first two gaps hold only two squares each, so the block must be in the last gap of four, which fills its middle two squares.

5. Crossing out when a line is complete

When the filled squares in a line already match its clue, every other square in it is empty. Cross them out: those crosses are what make progress on the lines that cross this one.

2 1Before
2 1After
The blocks 2 and 1 are both in place, so the rest of the row is empty.

6. Rows, then columns, then rows again

A single line rarely finishes on its own. The power of nonograms is that every square sits on a row and a column: something you learn from a row is new information for a column, and the other way round. So go through all the rows, then all the columns, and repeat until the picture is done.

1 1553124442The puzzle
1 15531244421. Rows
1 15531244422. Columns
1 15531244423. Rows
1 15531244424. Columns
A 5×5 puzzle solved in four sweeps. The squares each sweep decides are in orange. 1: the rows with clue 5 fill completely, and the 3 fills its middle square. 2: the columns with clue 2 are then complete, so their other squares are crossed out, and two of the columns with clue 4 gain a square. 3: the top row's 1 1 now has only three squares left, which decides it. 4: the bottom row follows from the columns.

Tips for bigger puzzles

  • Start with the longest clues. A line whose clue adds up to nearly its length gives the most in the first pass.
  • Count the gaps, not the squares. Late in a puzzle most lines are part-solved. Look at the runs of unmarked squares between crosses and ask which blocks can fit in each.
  • Match blocks to clues from the edges. The first block you can see from the left edge belongs to the first number, so it is often easy to complete it and move on.
  • Never guess. On this site every puzzle can be finished by these moves. If you are stuck, a line you have not looked at recently usually has something to give, and Hint will show you which one.

Try them on the puzzle at the top of this page, starting with 5×5. Deciding whether a general nonogram has a solution at all is an NP-complete problem, which is why puzzle makers check their grids; every puzzle here has been checked so these moves are enough.

Frequently asked questions

How do you solve a nonogram?

Mark only squares that are filled, or empty, in every arrangement that fits a line's clue. Start with long clues (the overlap rule), cross out lines that are complete, and alternate between rows and columns so each line's progress helps the lines that cross it.

What is the overlap method in nonograms?

Push the blocks of a clue as far left as possible, then as far right. Any square a block covers in both positions is filled. A single block longer than half the line always fills its middle.

Do you ever have to guess in a nonogram?

Not in a well-made one. Every puzzle on this site can be solved with line-by-line logic. Some hard printed puzzles need looking ahead several steps, but a good puzzle never needs a blind guess.

Where should I start a nonogram?

With the rows and columns whose clues add up to most of the line: they give the most filled squares straight away.

What does an X mean in a nonogram?

It marks a square you have worked out must be empty. Crosses are not part of the answer, but they make it much easier to see where blocks can still go.