Either you got really lucky or I'm really dumb :) -- because it took me a solid 6 attempts to solve the game. No matter what I started with, I always had 1 piece left over on all previous 5 attempts.
today's puzzle? I find it hard to fail unless I explicilty try. I can see but two dependencies in there (you need to connect the diamonds on the left and the circles on the right), and both are very easy to spot (one of them you're very likely to resolve even if you just click around).
Edit: ok, there are a few more dependencies, but they really easily resolve on their own.