Staring at an empty nonogram grid is the hardest moment of the puzzle, and it is entirely avoidable. There is a technique that fills squares with zero prior information, and every large grid opens with it.
The overlap
Take a row ten squares wide with a single clue of 7.
Push that run of seven as far left as it will go: it covers squares 1 to 7. Now push it as far right: it covers squares 4 to 10.
Squares 4, 5, 6 and 7 are covered in both extremes. Since the run has to be somewhere between those two positions, those four squares are filled — guaranteed, from nothing but the clue and the width of the row.
The general rule: for a single clue of length L in a line of width W, the overlap is 2L − W squares in the middle. So a 7 in a 10 gives 4. An 8 gives 6. A 6 gives 2. A 5 in a 10 gives zero, which is why the technique only helps on clues longer than half the line.
Overlap with several clues
The same idea works with multiple clues; you just have to account for the gaps.
Take a row of ten with clues 4 3. Pushed all the way left, that is squares 1–4 filled, 5 empty, 6–8 filled. Pushed all the way right, it is 3–6 filled, 7 empty, 8–10 filled.
Compare the two. The 4 covers 1–4 on the left and 3–6 on the right, so squares 3 and 4 are certain. The 3 covers 6–8 on the left and 8–10 on the right, so square 8 is certain.
Three squares filled before any real deduction. On a 15×15 grid this opening move typically fills thirty or forty squares.
Crossing off is half the game
Filled squares get the attention, but the crosses do just as much work — and most players badly under-use them.
A crossed square splits a line. A row of ten with one cross in the middle is two rows of four and five, and short lines have dramatically fewer possible arrangements than long ones. Every cross you place makes the crossing lines easier.
The practical habit: whenever you complete a run, immediately cross the squares at both ends of it. When you complete a whole line’s worth of clues, cross every remaining square in that line. It feels like busywork and it is where the next deductions come from.
Bounce between rows and columns
The single biggest inefficiency is trying to finish one line at a time.
Nonograms are solved by alternation. Fill what you can in a row, then immediately re-read the columns that row just touched — a newly filled square may have forced something four rows away. Then go back. A line you could do nothing with five minutes ago is often trivially solvable after two crossing squares appear.
If you find yourself stuck on a line, the information you need is almost always in the perpendicular direction.
Lines that are completely determined
Before anything else, scan for lines where the clues plus the mandatory gaps add up to exactly the line width. A row of ten with clues 4 2 2 needs 4 + 1 + 2 + 1 + 2 = 10 squares, so there is only one possible arrangement and the entire row can be filled immediately.
There is usually at least one of these on any board, and they are free.
Why any consistent grid counts
Our nonogram checks your grid against the clues rather than against the picture the generator started from. That is the mathematically correct rule: a puzzle is defined by its numbers, and if your filled squares satisfy every row and column, you have solved it — whatever the generator happened to have in mind.
Sizes run from a two-minute 5×5 up to a 15×15 that will take a proper sitting.