I believe a 'cook' refers to the key move whereas what you were talking about is known as a 'dual'.
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.
The solution can also be found by clicking the FEN which will take you to an online engine.
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. :)