Thank you. These are actually "chess constructs", a type of chess problem. You can also read about them on ChessBase or just google the term. I believe a 'cook' refers to the key move whereas what you were talking about is known as a 'dual'. Constructs aren't as strict and collectively, are generally designed to cater to players of all levels. The solution can also be found by clicking the FEN which will take you to an online engine.
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That's well possible. As English is not my mother tongue, I was seeking for a suitable term in a dictionary. Thanks for specifying that.
Right, but what I wanted to say, is, that giving the solutions together with the problems may seduce the readers to check them too early instead of really trying to solve the problems theirselves. :)