Everyone has their own preferences. Like you, I lose interest in puzzles after a few minutes. Whatever it is that gives some people great satisfaction out of finding that one missing piece, I didn't get it.
I can't speak to your experience, but for me, I like architecture. Finding the right way to glue pieces together is actually very interesting to me. I basically implemented reflection in C++ before I even knew that's what it's called because I thought it would be fun. I enjoy debugging and assembly optimizations.
What I found is that this speaks to the difference between a prototypical Software Engineer and Computer Scientist.
Engineers are interested in getting stuff done efficiently, and not just in CPU cycles--time for coding, training new coders, maintenance, extensibility, and how often the code will ever be run all must be taken into account. In my experience, grabbing someone else's solution via a package manager or using a 10-minute brute-force solution to a very hard problem can be the most "efficient". Just throw comments on it and avoid the puzzle so you can get something working. Of course, be sure to isolate the code so that if it ends up being a hotspot it's easy to fix later.
Computer Scientists, on the other hand, seek that efficient solution. Many of the PhD candidates I encountered were optimizing very specific cases of very hard problems (largely related to distributed computing). They enjoy spending time picking apart algorithms and understanding the problem so thoroughly that they can prove, confidently, that they have the most efficient solution to any given problem.
In the end, each broad category relies on its partner, and all programmers have to have some of both. Some of us just lean harder to one side than the other.
I have always enjoyed puzzles (although I rarely do them)--I think it's a part of something greater. I like to complete all the achievements in games. I like checking off tasks in task lists. I like cleaning my plate at dinner.
They all feel the same to me, and have little to do with how I operate as a computer programmer (speaking as a web application developer).