Here's a little "strategy" my friend found out, and is really handy if you want a lot of gold really fast. It's not as fun as taking your time doing it, but hey, designing your dream outfit is fun too, and with the money you can make off Jigsaw, you can get it in no time.
It works best on the Insane difficulty because the pieces are so small, and you can easily get upward of 600 gold a puzzle if you're a fast clicker. Basically, you collect all your puzzle pieces and put them all into a little pile. This is the time-consuming part; if it was like this at the start the Insane puzzles wouldn't take more than five minutes each. Then all you do is move one piece around on top of the pile, and the ones that connect will stick automatically. Once you've got a big chunk then put it to the side and start on another one. At the end, you should be able to fit the chunks together effortlessly, and figuring out where the rebellious pieces that don't want to stick isn't hard at all.