Useful solving composed mate-in-2 problems? I'm solving mate-in-2 puzzles from the Polgar 5334 problems book. 

Many of these are composed problems, and are hard (for me) to solve. Often I have to spend 10-15 minutes before finding the solution. Many time I don't find the solution in a reasonable time, and give up.

How useful are these problems for improvement, compared with solving more "normal" puzzles? And if they are useful, how much time should you spend on trying to find the solution? Are there some general procedure you should follow in order to find the solution fast?
I am going to re-post my exact answer to the question "Improving the observation skill &amp; making less blunders" with this preamble, because if you use them in this manner, you can cut down on mistakes early in calculation. Of course, this can be very helpful. If you learn to do this effectively, and as a matter of course in tournament games, you should see improvement.

In addition, you will see common patterns repeated, even if finding the first "key move" is difficult. I think scanning all possible moves, and not necessarily calculating deeply, depending on your current skill level, can lead to your solving these more quickly.

Here is that answer:

I will go back to what Artur Yusupov, three-time World Championship Candidate, former top-10 player,  and one of the greatest living trainers recommends in the first book of his 10-volume series. In volume one, "Boost Your Chess - Build Up Your Chess", chapter 9, which is two-move mates, including composed problems:


  The aim of this lesson is to improve your calculation of short
  variations. It is more important to find a lot of options in the
  first few moves than to calculate moves long variations. Most mistakes occur in the early moves in variations. What
  is the use of calculating a long and correct variation if your
  opponent has a much better reply on move one?
  
  You must develop your skill at calculating short variations, while at the same time taking into account the possibilities available to
  your opponent. This skill should reduce blunders.
  
  Exercises with mate in two moves are very well suited for training in
  the art of calculating short variations with great accuracy.
  Emphasis as written, not mine.


I will take this one step further with my own suggestion. Try to train yourself that before you make every move, look at EVERY move your opponent has. I am not saying that you are calculating anything. You are simply looking at it so you consider it. It will do two things: If you are hanging a piece, just looking at it will usually "hit you in the face like a brick", and second, I have done many combination problems over the last 40 years, and sometimes, when I cannot figure it out, and look at the answer, I realize immediately that had I just LOOKED at the move, I would have seen the combination.

So, again, you are not trying to calculate, just consider every move. You will be amazed at what you register immediately.