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.

Edit 4: I sympathize with the advice below to be generous but for the sake of discussion let me play the devil's advocate and consider various ways this can lead to injustice and even corruption. These are not all directly related to the original question but take into account what has been said in the comments below. Since I can not answer my own question because it is on hold, I will list them here.

• The advisor Alice could teach Charlotte a bad lesson - if you continue to discuss problems with enough people, you can make a career out of it. I know several cases of collaborations like this, including when the person doing most of the work ends up at a less prestigious university.

• It could be a perfectly ordinary situation that several people get to be authors even if all the ideas that finally led to the solution came from only one of them. But this is not so far from an all-too-common situation when briefly discussing a problem at a conference with a random person leads to this person being a coauthor while contributing essentially nothing.

• What happens if a seniour mathematician is so motivated to promote his field that his doctoral students or postdocs end up at top level universities relying mainly on someone else's work? This can happen when the seniour mathematician has power, and I personally know such a case.

• It is not uncommon for a known and difficult problem to be solved shortly after a breakthrough that provides the missing piece. Most of the credit goes to the author (often sole) who takes the final step, even when the preceding advance is crucial. Where is this threshold when the joy of collaboration becomes less desirable than credit?