[sumul]

I think this is a excellent question that I haven't been asked before. I don't have a great answer, as I don't consider myself to be particularly great at solving these puzzles. Some of my friends are consistently better (fewer tries, faster) than I am. I've noticed that I find important patterns and key moves more quickly now after playing so many of them, but sometimes I still get stumped. Often I realize that I make an assumption about a large group needing to be cleared at once, but the solution hinges on intentionally breaking up the large group to make something else happen a move or two later. I think it's really fun to learn these types of things by experience, so my main suggestion—if you find it fun and not too frustrating—is to approach each puzzle with an open mind and don't get too attached to any single moves that you believe to be correct. Finally, you've probably noticed that you're often left with the same one or two tiles when you run out of moves. Try to think ahead and see if there are ways to connect that tile to another one earlier. Good luck!