Working with two different set of colleagues on the same problem I am a Ph.D. student working on Computer Science. This is the situation. I thought of an interesting problem, and had a discussion about it with someone (call this person A) I wanted to establish a connection with. We discussed some ideas but they failed. We then stopped talking for a while.
Few weeks later I discuss this problem with another person, B, a postdoc at my group. We see no way of making progress in the first meeting. Then B tells me that C, a PhD student at my group, is also interested in the problem. We start having regular meetings the three of us (B, C and myself) and slowly make progress with the problem.
Then, after some months of silence, A contacts me proposing some early solutions to the problem that seem promising, clever and way more sophisticated than what B, C and I have been thinking of.
At this point I don't know how to proceed. Ideally, we could work on the problem the four of us, but it is unfair in light of the fact that the deepest contributions come from A, and the other three of us would be around just to help establishing the results and presenting them (A is an expert in a different field so it does need the help of one of us to make their techniques relevant, but three of us is too much I think). On the one hand, I have held discussions with B and C, which have led to essentially zero progress, but they have been interested in the topic nevertheless. Leaving them to (re)join A also sounds a bit inappropriate.
Any suggestion or advice is more than welcome. I can help clarifying the situation even more if you feel it's needed.
Actually, you should let A know that you and the others have been working on the problem and propose that you merge into one group. If B and C haven't been productive on it, then you might want to discuss it with them first. It might be that one or both of them isn't ready for a more intensive collaboration.
You can, jointly, be honest with A that your progress has been slow.
But it would be a mistake to arbitrarily exclude anyone.