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?