A chess problem is a puzzle or brain teaser, which are not copyrightable. This comes from a mix of functionality and merger doctrines. Functional works, like forms or layouts are not copyrightable. Works which have only one way to express or only a few ways to express are not copyrightable. A chess problem is a layout of chess pieces, and there is only one or a few ways of expressing a particular problem, and hence would not be copyrightable. If the annotations to the problem merely describe what is going on in the puzzle they would probably not be copyrightable either, although if they added alot of language flourishes then they may be copyrightable. A collection of chess problems may be copyrightable as a compilation. A compilation of non-copyrightable works may be copyrightable in itself, but this copyright is very thin and would only be infringed by taking a large number of the problems out and republishing them (you might even have to republish them in sequence).
- All this only applies to U.S. copyright, and I'm not a lawyer, but I am in law school to become an intellectual property lawyer.