Every nonogram on Pencil Grids can be solved one line at a time. These are the line techniques that get you through a 15×15 or 20×20 without guessing.
1. Overlap with several clues
Push every run as far left as it can go, then as far right. If a run's two positions overlap, those cells are filled. Do this for every line at the start. On big grids it can fill a lot.
2. Edge forcing
If a filled cell sits close to the edge of a line, the first run must cover it. With a clue starting "4" and a filled cell in position 2, the run of four must cover position 2, so it can't end before position 4. Cells 2 to 4 are filled. Then work inwards.
3. Completing and capping runs
When a stretch of filled cells is as long as the biggest clue that could fit there, it's complete. Cross the cells at both ends. Capping runs is the main source of crosses, and crosses unlock the crossing lines.
4. Too small to fit
A gap between crosses that's shorter than every run that could go there must be empty. Cross it out. Near the edges this happens all the time.
5. Joining and splitting
Two filled cells with one unknown between them: if joining them would make a run longer than any clue that could cover them, the middle must be a cross. If they must belong to the same run, fill the middle.
6. Which run is this?
For each filled stretch, ask which clue numbers could be responsible for it. Often only one can, because the runs before it need room. Once you know a stretch belongs to a particular clue, the overlap trick applies to that run alone.
7. Keep sweeping
Every new mark can unlock the line that crosses it. Experienced solvers work in sweeps: all rows, then all columns, and repeat. Our hint button follows exactly this order.