A nonogram can look stuck even when its next move is already forced. Before guessing, look for a line whose remaining placements agree on a cell, finish any runs you can prove complete, and carry each new mark into the crossing line. A blank square is still undecided; an × is a claim that the square must stay empty.
This guide uses the 5×5 Arrow puzzle from our practice collection. You can open it without revealing its answer. The examples below explain a few deductions rather than showing the completed picture.
First, separate what you know from what you expect
Choose one row or column and read its clues in order. A clue of 3 requires exactly three consecutive filled squares. Two clues, such as 2 and 1, require separate groups with at least one empty square between them. Extra empty squares may appear before, between, or after those groups.
Ask yourself why each existing mark belongs there. “It would make the picture symmetrical” is an expectation, not a deduction. A picture may turn out to be symmetrical, but the clues are the evidence. If you made a tentative mark, undo it before using it to rule out other possibilities.
For a quick space check, add the group lengths and the minimum separators. Clues 3 and 1 need five cells: three filled, one empty, then one filled. In a five-cell line that determines every position. In a longer line, the same clues have room to move.
Find the overlap, not the most attractive placement
Consider a five-cell row with a single clue of 3 and no marks. There are only three ways to place its run:
| Placement | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 1 | ■ | ■ | ■ | × | × |
| 2 | × | ■ | ■ | ■ | × |
| 3 | × | × | ■ | ■ | ■ |
3 legal placements. ■ filled; × empty. These rows are alternatives, not consecutive moves.
Position 3 is filled in all three placements. Positions 2 and 4 are filled in two placements, but “two out of three” is not certainty. Mark only position 3 as filled. Leave the others undecided until you gain more information.
For a single uninterrupted run of length L in an otherwise unknown line of length N, the overlap has length max(0, 2L − N). In this example, 2 × 3 − 5 = 1. That shortcut does not replace checking multiple groups, mandatory gaps, or existing marks.
The useful habit is to compare the earliest and latest legal positions. If a cell stays inside the run in both extremes, it belongs to the overlap. If known empty cells block one of those extremes, recalculate within the remaining legal space.
Let another line remove the uncertainty
In Arrow, row 3 has clue 5 and column 3 has clue 5. Each fills its entire five-cell line. That gives you a cross, but it is not yet the complete picture.
Now inspect columns 1 and 5. Each has clue 1, and row 3 already supplies that filled cell. Every other cell in those columns must therefore be empty. In particular, both ends of row 2 are empty.
Row 2 has clue 3. With its ends excluded, its middle three cells are the only possible run:
| Placement | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 1 | × | ■ | ■ | ■ | × |
1 legal placement. ■ filled; × empty. These rows are alternatives, not consecutive moves.
Notice what solved the row: not a guess about the picture, but two empty marks proved by other columns. Whenever a row changes, revisit the columns crossing its new marks. Whenever a column changes, revisit the affected rows.
Close a run only when you know which clue it satisfies
If a line has one clue of 3 and its full three-cell run is established, all remaining cells are empty. With several groups, be more careful. A visible run of two might already satisfy a clue of 2, or it might be the unfinished beginning of a clue of 4.
Before putting an × beside a run, identify its matching clue and prove that the run cannot extend. Otherwise, the separator itself can become the mistake that makes the puzzle seem impossible. Our empty-cell mistakes guide shows how to recognise that failure.
Use a short stuck-check routine
- Recheck the clue order and the difference between blank and ×.
- Look for a full line, a zero clue, or a run that uses all remaining space.
- Compare legal placements and mark only cells on which they all agree.
- Close completed runs when their clue assignment is certain.
- Revisit crossing lines after every change.
- If no move appears, use one explained hint and read its reason before continuing.
A unique answer does not promise that every step is an easy overlap. Some puzzles need reasoning across several lines. Our hint explanation describes how this site's hints handle that distinction.
Practise the deduction, then finish the picture
Open Arrow. Fill the full middle row and column. Before touching row 2, work out which columns prove its outer cells empty. Then explain, in your own words, why the middle three cells must be filled.
Your progress may already be saved in this browser. If you want a fresh attempt, use Restart and confirm that you want to clear this puzzle's marks. When you are ready to check the rest, the complete five-step walkthrough shows the same puzzle from start to finish. For a larger example, move on to the 15×15 walkthrough.