Rif Brachot 37a

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37a

{Brachot 50a continued}
Gemara:
Why do we need this {the start of the Mishna, which stated: IF THREE PERSONS HAVE EATEN TOGETHER THEY MAY NOT SEPARATE [FOR GRACE]. }?
We learnt it already once: Three who have eaten as one are required to say the zimmun.
R Abba cited Shmuel: This is what it means to teach: Three who have sat down to eat, even if each one eats of his own loaf, they are not permitted to separate.

Or else, like Rav Huna, who said: Three people who come from three separate groups may not separate {even though they have not actually eaten together}.

And Rav Chisda said: And this is where the other two {of each original group} did not preempt and make a zimmun with him {even though he himself did not say Grace}. But if they did preempt and make a zimmun with him, the zimmun already flew away from them {these three composed of one from each group}.

MISHNA:
IF TWO GROUPS EAT IN THE SAME ROOM, AS LONG AS SOME OF THE ONE CAN SEE SOME OF THE OTHER THEY COMBINE [FOR ZIMMUN],
BUT OTHERWISE EACH GROUP MAKES ZIMMUN FOR ITSELF.

{Brachot 50b}
Gemara:
A Tanna taught: If there was an attendant between them {the two groups} he causes them to combine.