NonogramSolver

How to Solve Nonograms

Nonograms (also called picross, griddlers, or hanjie) are logic puzzles where you fill cells in a grid to reveal a picture — using only numbers as clues. No guessing required. This guide takes you from zero to solving medium-difficulty puzzles confidently.

What is a nonogram?

A nonogram is a grid — typically square, anywhere from 5×5 to 25×25 cells — where some cells are filled and others are left empty. The filled cells form a hidden picture. Along the top of the grid are column clues, and along the left side are row clues. Each clue is a sequence of numbers.

Each number in a clue tells you the length of a consecutive run of filled cells in that row or column. The runs appear in the order listed, left-to-right (for rows) or top-to-bottom (for columns). There must be at least one empty cell between any two runs.

Example: A row clue of 3 1 2 in a 10-wide row means: somewhere in the row, there is a run of 3 filled cells, then at least one empty cell, then a run of 1 filled cell, then at least one empty cell, then a run of 2 filled cells.

The rules in full

  • Each row and column has an independent clue sequence.
  • Runs must appear in the exact order given — you cannot reorder them.
  • At least one empty cell must separate consecutive runs.
  • A clue of 0 (or a blank clue) means the entire row/column is empty.
  • Every valid nonogram has exactly one solution that satisfies all clues simultaneously.

Step 1: Start with the most constrained lines

Before touching a pencil, scan all rows and columns for lines where you can immediately deduce some cells. The most constrained lines are those where the clue sum is close to the line length.

The minimum space required for a clue sequence is the sum of all run lengths plus one separator between each pair: for clue 3 1 2, that's 3 + 1 + 1 + 1 + 2 = 8 cells minimum. If your row is 10 wide, there are only 2 "slack" cells to play with.

A clue that requires the entire line has zero slack — every cell's state is fully determined. A clue of 5 in a 5-wide row means every cell is filled.

Step 2: Simple overlap (the core technique)

The simple overlap method works by finding cells that must be filled regardless of which valid arrangement you choose. Here's how:

  1. Slide the clue as far left as possible (leftmost valid position).
  2. Slide the clue as far right as possible (rightmost valid position).
  3. Any cells covered by both extremes must be filled.

Example: Clue 4 in an 8-wide row. Leftmost: cells 1–4 filled. Rightmost: cells 5–8 filled. Overlap: cells 5 through 4 — wait, that's cells 5 to 4 which is backwards, so there's no overlap here. Now try clue 6 in the same 8-wide row: Leftmost: cells 1–6. Rightmost: cells 3–8. Overlap: cells 3–6 must be filled.

The overlap grows as slack decreases. With clue 7 in 8 cells, cells 2–7 must be filled (6 cells determined from one clue).

For multi-run clues, apply the same logic to each run in sequence, carrying forward the minimum starting position of each subsequent run. Read the full simple overlap technique guide for detailed worked examples.

Step 3: Use known cells to constrain further

Once you fill some cells using overlap, those cells become constraints for the perpendicular lines (rows constrain columns and vice versa). This is the iterative heart of nonogram solving: every deduction in one direction enables new deductions in the other.

Work through rows, then columns, then rows again. Each pass narrows the possibilities until the puzzle is solved.

Step 4: Block capping

When a filled run reaches exactly the length specified in a clue, the cells immediately on either side of that run must be empty. This is called block capping.

Example: if clue is 3 and you've determined three consecutive filled cells, the cell to the left of the first filled cell and the cell to the right of the third must be marked empty. This frequently unlocks adjacent clue runs.

Learn more: Block capping technique.

Step 5: Clue exhaustion

When the total number of filled cells in a line equals the sum of all its clue values, all remaining unknown cells in that line must be empty. This is a cheap check to run after every deduction.

Example: clue 2 3 requires 5 filled cells total. If you've already confirmed 5 filled cells in that row — even if they're not all grouped yet — every remaining unknown cell must be empty.

Step 6: Edge deduction

If a filled cell appears very early in a line (near the left or top edge), it must belong to the first clue run. This lets you determine the extent of that run and potentially cap it. The same logic applies to filled cells near the right or bottom edge — they must belong to the last run.

Learn more: Edge and endpoint deduction.

Step 7: Contradiction method (advanced)

For harder puzzles, constraint propagation alone may not be enough. The contradiction method involves tentatively assuming a cell is filled, running all the above techniques, and checking whether a contradiction results (a line becomes unsolvable). If it does, the cell must be empty — and vice versa.

This technique is powerful but slow to do by hand. Our solver applies it automatically when the other techniques stall. Read the contradiction method guide to understand when and how to apply it yourself.

Common beginner mistakes

  • Marking cells too early. Never fill a cell unless you're certain — a wrong fill can cascade into many wrong deductions. Use a light pencil mark for "possibly filled" cells and only commit when certain.
  • Forgetting that runs must be in order. Clue 2 3 cannot have the run of 3 appear before the run of 2 in the same line.
  • Not checking both directions. After every row deduction, immediately check the affected columns — the cross-deduction is often where the puzzle opens up.
  • Ignoring zero-clue lines. A blank or 0 clue means the whole line is empty. Mark every cell in that line immediately.

Practice puzzles

The best way to learn is by doing. Try our collection of free nonogram puzzles organized by difficulty — start with 5×5 easy puzzles and work up to 15×15 hard ones. If you get stuck on any puzzle, our solver can show you the exact step that unlocks it.

What's next?

Once you're comfortable with the basics, explore the individual technique guides:

Or jump straight to the solver and try it on your own puzzle.