This post is a sequel to: Collaboration or acknowledgment?

The following has come to my attention. A senior mathematician (let us call him or her Alice) suggested a problem to a young mathematician (Bobby) who proceeded to solve it on her own and wrote up the result. Bobby agreed to let Alice be listed as a coauthor, but Alice also insisted to include her PhD student (Charlotte) as a coauthor because they were thinking about the same problem, despite the fact that Alice and Charlotte did not even have partial results. Is there a way for Bobby to manage such a situation without creating conflict?

Edit 2: Bobby had no problem with Alice joining her as a coauthor for the reasons mentioned by Igor Rivin below (I include you as a coauthor, you write me a good recommendation). Thus, the credit was unfairly diluted by including Charlotte who had not contributed. Igor Rivin also mentioned that this is not a new phenomenon, which I am surprised to hear.

Edit 1: One good advice so far is to be generous. It does reward unethical behaviour but I have no better advice for Bobby, which is why I asked this question.

Edit 3: I do not agree that it is not useful to discuss these issues in a public forum. If, as a community, mathematicians denounced such unethical practices, they would be less likely to occur.