@GerhardPaseman: I accept your criticism and promise to never ask another question on this forum. Nevertheless, the whole process has been extremely helpful.

@AndréHenriques: In addition, I have never actually seen myself how bad this problem is, so there is a chance that I will have to confront Alice in the future.

@AndréHenriques: It may come to that, but first I try to give good advice and let Bobby handle this herself and try to resolve it amicably. The discussion here has given me a good perspective of the variety of attitudes that people have, and why one should to be careful.

@AndréHenriques: I'm not afraid of Alice. I do not want to cause any problems to Bobby later on, but I can assure you that I am doing my best to handle the situation indirectly.

What if the problem does not come from Alice? If several people have already worked on it without discovering the answer? If Alice mentioned it to Bobby as an interesting problem that people care about? What happens if you discuss a problem with someone at a conference and then solve it without any of the ideas from that conversation? Honestly, I can think of more cases where it is definitely not a collaboration than where it is.

@ToddTrimble: Fair enough. I thought the meaning was clear from the context, but clarification is needed. By the way, Igor Rivin's comment was added later to give an idea why including Alice as a coauthor is somewhat justified.

@ToddTrimble: Please read carefully what I wrote. A insisted. B did not mind given the situation. Of course B should have been the sole author.

@YemonChoi: I have edited following people's suggestions and never changed the gist of the question. Why is it disingenuous? And why is the question still on hold?

@ToddTrimble: It was just a joke.

@NoahSnyder: This is a very good point that most people forget. C has a say, but in the example I am talking about, C is neither as innocent nor as noble as you.