Sort by colour first, shape second
On a physical puzzle most people start by separating the edge pieces. On a browser puzzle the edges are less interesting because the snap-to-grid catches mistakes quickly. What helps more is a fast first pass sorting by dominant colour — sky pieces in one mental zone, water in another, foliage in a third. Once you're working inside a colour family, finding shape matches gets dramatically faster.
Build small islands, then connect them
Trying to solve a puzzle linearly from one edge to the opposite is slow. Faster solvers build 3-to-5-piece islands of obvious matches anywhere on the board — the bright spot on a wave, a face, a window frame — and then bridge between them. Islands give you anchor points that the rest of the picture organises around.
Use the picture as a map
Turn on the Preview toggle in the puzzle player when you genuinely need it (not as a crutch). A glance at the full image tells you which region a stray piece belongs to in seconds. Closing the preview again forces you to do the local matching from memory, which is where the cognitive workout actually lives.
When you're stuck, take a break
Five minutes away from the screen is worth twenty minutes of staring at the same orange patch. Visual fatigue is real — the longer you look at a region, the harder it is to see fresh combinations. The board state is saved in your browser, so close the tab and come back to a piece that, somehow, is now obviously a sleeve.