Berachos, Chapter 7, Mishnah 4. This mishnah deals with a single principle: once a person has become obligated in zimun - and even in a particular form of zimun - he may no longer separate from the group and recite the berachah on his own without zimun, or without that particular form of zimun.
The text of the Mishnah:
"Sheloshah she'achlu ke'echad einan rasha'in leichaleik, vechein arba'ah, vechein chamishah. Shishah nechlakin ad asarah, va'asarah ein nechlakin ad sheyihyu esrim" - three who ate together may not separate, and so too four, and so too five. Six may separate, up to ten, and ten may not separate until there are twenty.
Three who ate together may not split up and have each one recite the berachah on his own, because they became obligated in zimun. Zimun is not a matter left to a person's choice, to be done if he wishes; rather, from the moment they ate together, an obligation rests upon them to recite the berachah together in the form of zimun. The same law applies to four who ate together, and the same law applies to five.
The levels of separating:
Three, four and five - they may not separate, since in any division there would remain a group that does not contain three, and the obligation of zimun would lapse from it.
From six up to ten - they may separate, for six can split into two groups of three, and each of them will fulfill the obligation of zimun that they became obligated in.
Ten - they may not separate, until there are twenty.
The reason that ten may not separate:
Ten who ate together cannot split into two groups, because if one of them has ten or more, the second will not have ten. The result would be that the members of the group that has ten would be able to say "Elokeinu," while the others would not be able to - and yet all of them became obligated in a zimun that includes the word "Elokeinu." For this reason they do not have the ability to split, until there are twenty.
Once they are twenty, and each of the groups will have ten, each one of them will be able to say "Elokeinu," and in that way the obligation of zimun that they became obligated in will be fulfilled.
In summary: In this mishnah we learned that zimun is an obligation and not an option, and therefore those seated at the meal may not separate from the group unless the obligation of zimun that they became obligated in is preserved in each of the groups, and to the same degree. Three, four and five do not separate; from six up to ten they may separate; and ten do not separate until there are twenty, so that even after the division all of them will be able to say "Elokeinu."