Nonogram rules

What is a nonogram?

A nonogram is a logic puzzle played on a rectangular grid. Each row and column has a set of number clues that describe the filled cells in that line. The numbers indicate consecutive groups of filled cells, in order. Between each group there must be at least one empty cell.

Your goal: determine which cells are filled and which are empty, using only the clues and logical reasoning. When the puzzle is complete, the filled cells form a pattern (sometimes recognizable as a picture on larger grids).

The puzzle has many names. Nintendo calls it Picross. In the UK, it's often called a Griddler. In Japan, Hanjie. You might also see "pixel puzzle," "paint by numbers," or "pic-a-pix." People sometimes misspell it as "nanogram" or "nonagram." They all refer to the same thing.

Rules at a glance

1. The grid is rectangular. Each cell is either filled or empty.
2. Each row has a clue: a sequence of numbers describing the consecutive groups of filled cells in that row, left to right.
3. Each column has a clue: a sequence of numbers describing the consecutive groups of filled cells in that column, top to bottom.
4. Each number represents one group. Groups are separated by at least one empty cell.
5. A clue of [0] means the entire line is empty.
6. The puzzle has exactly one valid solution.

How the clues work

Let's say a 5-cell row has the clue [2 1]. That means:

• A group of 2 filled cells appears first (left to right).
• Then at least 1 empty cell.
• Then a group of 1 filled cell.

The minimum space required is 2 + 1 (gap) + 1 = 4 cells. Since the row is 5 cells wide, there's 1 extra cell of slack. The group of 2 could start at position 0 or 1, and the group of 1 adjusts accordingly.

Now consider a clue of [3] on the same 5-cell row. The group of 3 could go at positions 0–2, 1–3, or 2–4. That's three possible placements. The only cell covered by all three is position 2 (the center cell). So you can fill that cell with certainty — even without looking at any other clue.

That reasoning is called overlap logic, and it's the most important solving technique.

Overlap logic (the core technique)

For each clue group in a line, imagine sliding it to its leftmost valid position, then to its rightmost valid position. The cells where these two placements overlap are guaranteed to be filled.

Example: clue [7] on a 10-cell row.

• Leftmost placement: cells 0 through 6.
• Rightmost placement: cells 3 through 9.
• Overlap: cells 3 through 6 are filled in both. Fill them.

Larger clues relative to the line give bigger overlaps. A clue of [9] on a 10-cell line overlaps 8 cells. A clue of [2] on the same line overlaps zero. For short clues, you need other information (from crossing lines) before overlap produces anything.

Filling cells vs. marking X

You have two actions: fill a cell (meaning it's part of a group) or mark it X (meaning it's definitely empty). Both carry information. Don't skip the X-marks.

When you determine that all groups in a line are satisfied — the filled cells already match the clues — mark every remaining empty cell in that line with X. The game auto-strikes through the clue when this happens, which helps you keep track.

Each X you place constrains the crossing line. An X in row 3, column 5 tells column 5 that cell (3,5) is empty. That may narrow where column 5's groups can go, producing a new overlap. This is how large puzzles get solved: the information propagates back and forth between rows and columns.

Edge logic

If you know the first cell of a line is filled, the first clue group must start there. If the first clue is [3], fill cells 0, 1, 2, and mark cell 3 as X (mandatory gap).

Same idea at the right end with the last group, and at both ends of columns. Edge deductions are often the easiest to spot and frequently chain together: filling a cell at one line's edge creates a filled cell in the crossing line, which may be at that line's edge too.

Gap analysis

Once some cells are filled or X-marked, the line breaks into segments of consecutive unknown cells. Check each segment:

• If a segment is shorter than the smallest remaining group, every cell in it must be empty. Mark with X.
• If a segment exactly matches a group's length, the group goes there. Fill it and X-mark the boundaries.
• If a segment is longer than the group, apply overlap logic within that segment.

Gap analysis is what turns a partially solved puzzle into a cascade of forced placements. It gets more powerful as you fill in more cells.

Common mistakes

Forgetting the gaps. Groups must be separated by at least one empty cell. A clue of [2 2] on a 5-cell line doesn't mean "fill 4 cells anywhere." It means: 2 filled, 1+ empty, 2 filled. The minimum space is 5 cells, so there's only one valid placement.

Not X-marking completed lines. When a line's clues are satisfied, all remaining cells must be empty. Forgetting to mark them means you miss information that the crossing lines need.

Guessing. If you can't determine a cell, don't guess. Move to another row or column. There's always a deducible cell somewhere on the board. Our puzzles are verified solvable through logic — if you're stuck, the information is there. Try the hint system.

Solving a 5×5: step by step

Here's how you'd approach a simple 5×5 grid:

Step 1: Scan for full lines. Check if any row or column has a clue that equals 5 (fill the whole line) or 0 (X-mark the whole line). Fill or X-mark them immediately.

Step 2: Apply overlap logic. For each remaining line, check if the clue is long enough relative to the line to produce an overlap. On a 5-cell line, any single group of 3 or more gives guaranteed cells.

Step 3: Cross-reference. After filling cells from overlap, check the crossing lines. A newly filled cell in row 2, column 4 gives column 4 more information. Recheck that column.

Step 4: Repeat. Alternate between rows and columns, applying overlap, edge logic, and gap analysis. Each pass fills more cells. On a 5×5, the puzzle usually resolves within two or three full passes.

Frequently asked questions