That mostly depends on the problem and on the outcome/conclusions of the impromptu meeting: sometimes the conclusion and the decided course of action is so cut-and-dried that, essentially, the problem that was no longer is. In that case, usually only one person continues with the actual implemention. In other cases, the result of the meeting is an avenue to explore via coding, and in that case we continue attacking or unravelling the problem together, behind a computer.
This flexible and adaptable approach sounds entirely reasonable to me.
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