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.
RE: Computer-Generated Chess Problem 02636