Method to study chess puzzles way above your level I have a collection of middle-game chess puzzles classified in levels. I can solve most puzzles in the first level after a few minutes, and some of the puzzles in level 2.

But for higher levels there is no hope I can solve any of them, even if I tried for a thousand years. Nevertheless, those are supposed to be interesting positions with hidden treasures, and I wonder if I can still learn something from them. What should I do? Play against a computer from those positions until finding the solutions? Look at the solutions and memorizing them?
Chess puzzles (and to a large extent playing chess) are based around recognizing certain patterns or motifs which help you to quickly assess a position and to visualize potential lines without the need to calculate move by move in your head. 

Chesstempo has a good list of tactical motifs and positional motifs. It is important that when you solve problems (or when analyzing your games) that you realize which motives (usually there is more than one) apply to this problem. If you cannot solve a problem on your own it is fine to look up the solution or to get help from a computer, but make sure you understand the solution (i.e. match them to motifs/patterns). Again chesstempo is very useful for this as it shows you the motifs of each problem as "tags" (after you solved it or after you failed to solve it).

Once you have built a repertoire of patterns/motifs in your mind you should have a good basis to solve more complicated problems as well.

Another factor could be visualization when calculating long lines, but there is not much you can do about it other than concentrating, playing games, analyzing games, solving puzzles.... basically everything you should be doing anyway.