How to Solve a 5×5 Nonogram Without Guessing

The useful news for a beginner: you can make steady progress without guessing. Start with lines whose clues leave only one possible shape, then carry those certain squares across the grid.

1. Read a clue as groups, not a total

A clue of 3 means one run of three filled squares next to one another. A clue of 2, 1 means a run of two, followed later by a separate run of one.

Separate groups need at least one empty square between them. So 2 + 1 + 1 required gap = 4 cells at minimum. Their order cannot change.

2. Fill a line that is already certain

On a 5×5 line, a clue of 5 fills every square. A clue of 0 leaves every square empty. These are the best first moves because there is no choice to make.

After filling a complete run, mark the squares immediately outside it as empty when the line has room. An × mark is a reminder that a filled square cannot go there.

3. Use the minimum-space test

For clues 2, 1 on five cells, the groups and their required gap use four cells. There is only one cell of flexibility. Compare the placements from both ends: any square filled in both placements is safe to fill.

4. Look for overlap

Suppose a 5×5 line has a single clue of 4. The run can begin in the first cell or the second cell:

The middle three cells are filled in both possibilities. Fill those overlapping cells, even though you do not yet know which end the run uses.

5. Mark empties to make crossings useful

Filled squares tell you where a run must pass. Empty marks tell you where it cannot pass. When a row already contains all the filled squares required by its clue, mark every other unknown square in that row as empty. Do the same for a completed column.

A line can match its numbers while still allowing more than one arrangement. Let the perpendicular clues confirm the positions.

6. Alternate between rows and columns

1. Find a certain row or column.
2. Fill its certain squares and mark its certain empties.
3. Read the crossing clues again.
4. Repeat until the picture is complete.

If you get stuck, review lines containing a new filled square or × mark. Use Undo if a mark was accidental; a pause is better than a guess.