I have an overactive mind, to say the least, so I need to keep it engaged or it bothers me.
I like Tangram. It's not really a "puzzle" in the Western sense, and is best approached as something that can be used to seek balance and understanding, rather than a problem to be solved and then discarded.
Even though I work to use the seven pieces to match silhouettes in a book, the approach is just very different from a western puzzle. Smart people who think about the deep math and elegant balance of order/disorder of the seven pieces could explain it better than a vaped dude can right now.
The real "a-ha" moment came for me when I realized that no matter how hard i tried as long as I lived, I will likely never come up with a more expressive chicken than some anonymous person in China did hundreds of years ago when all the basic forms were perfected.
But you can always try! And I do it all the time, and never until tonight did I come up with something on my own that made me smile because it was so beautiful in its symmetry made from the most asymmetrical configuration I could imagine. Although I've "solved" countless similar geometrical forms, and this one is probably in one of my books, it still came out of me and at least I think that's kinda cool.