Suppose than person A comes up with an interesting task, but is not able to solve it. Then, A sends this problem to his friend B and asks for help in solving it. After B successfully does that, the question appears: whose problem is that, A's or B's?
I don't like the approach when A is considered an author as in that case he can, for example, just spam B with tons of statements he just came up with without any intuition if those are solvable, and that doesn't sound as highly intellectual work. From the other hand, I don't like approach when B is considered the author too: he is doing the same amount of job as any contestant would do during the contest. A more interesting example: if A sends his problem to both B and C and they solve it with a difference of 5 minutes. Would be weird to say they both are coauthors, would be weird to say that the first one who solved is author either.
To avoid confusion, I just prefer not to share my unsolved problems with anyone, but in this case, some interesting problems may be lost. What are your thoughts on this question?
What do you mean by authorship of the problem? Formally, A is the author. But the fact that someone is the author of the problem, does not mean that B makes less investment to the problem. For example, C may prepare this problem and spend lots of time on it, but obviously, that does not makes him the author, it makes him preparation man. For B it is the same, he is just a person, who solved the problem. Can't see any reasons to think otherwise.
A should have some claim to authorship if he shared a creative and well-formulated problem statement with B. It's not that easy to spam such ideas.
It would be A. Spamming low quality problems doesn’t make someone not an author. It just makes them a really bad author.
But seriously, quite often I co-author some problems, because I just discuss some possible ideas with other people. And I guess this is fine. If someone had some cool idea, and someone else had a cool solution, they both contributed to the cool problem.
A is the author of the problem, B is the author of the solution.
In SPbSU, we use the following system:
The person who came up with the idea of the problem is the problem author. Good ideas are scarce and therefore important.
The person whose responsibility is to turn an idea into a contest problem is the problem developer. Often it means preparing the bulk of the problem, and only asking for help with alternative solutions. Other times, it means delegating: the statement is written by Alice, the solutions by Bob, and the tests are prepared by Carol. Anyway, the developer's responsibility is to ensure that all parts of the problem are done, and they are consistent.
In the published problem statement, the developer takes the credit.
Picking problems to use in a contest is a collective endeavor: the authors share their ideas, and the possible solutions are discussed. The authors can then choose to develop their own problems, or to delegate them to other developers.