How to solve a nonogram: the line logic that never needs a guess

To solve a nonogram, work one line at a time: use the clue to find which cells in that line must be filled and which must be empty, then move to the lines that cross it. Every Gridarium nonogram can be solved this way, so you never have to guess.

How to read a clue

The numbers beside a row, or above a column, give the lengths of the runs of filled cells in that line, in order. A clue of 3 1 means a run of three filled cells, then at least one empty cell, then one filled cell. A clue of 0 means the whole line is empty.

Technique 1: the overlap

When a clue is long for its line, some cells are filled wherever the run ends up. Slide the run as far left as it goes, then as far right: the cells that are filled both times are certain.

With a clue of 7 in a line of 10 cells, the run can start at any of 4 places. Whatever it does, cells 4 to 7 are filled.

Technique 2: a clue that fits exactly

Add up the runs and one gap between each. If the total is the length of the line, there is only one way to place them, and the whole line is solved.

A clue of 2 1 3 needs 8 cells in a line of 8: it fits exactly. The line is filled, filled, empty, filled, empty, filled, filled, filled.

Technique 3: use what the crossing lines told you

Every cell you settle is a new clue for the line that crosses it. A filled cell next to the start of a short run tells you where that run is, and the cells beyond its reach must be empty.

A clue of 2 in a line of 5, with cell 2 already filled. The run has to cover cell 2, so it cannot reach cells 4 to 5: they are empty.

Mark the empty cells

Use the Mark empty tool for the cells you know are empty. They do not count for the solution; they just stop you reading the same line twice. A clue turns grey when the filled cells of its line match it, so you can see what is left to do.

The levels on Gridarium

• Easy: a 5 by 5 grid.
• Medium: a 8 by 8 grid.
• Hard: a 10 by 10 grid.

Pictures are mirror images, left and right, which makes the clues of a column match the one on the opposite side. The puzzle of the day follows the week: easy on Monday and Tuesday, medium from Wednesday to Friday, hard on the weekend.