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1)

(a) Two people who ate together are not obligated (perhaps not even permitted) to Bensch Mezuman, three are.

(b) The Chidush of all the cases in the Mishnah, where people who seemingly ate ba'Aveirah, may nevertheless combine for - and even Bensch - Mezuman, is that it is not considered a Berachah ba'Aveirah (which in turn, is referred to as an insult, rather a Berachah).

(c) According to the Tana Kama, one has to have eaten a Kezayis in order to Bensch Mezuman, according to Rebbi Yehudah, a Kebeitzah.

(a) Rebbi Avahu learns Mezuman from the Pasuk "Ki Sheim Hashem Ekra, Havu Godel l'Elokeinu".

(b) We also learn from "Gadlu la'Hashem *Iti*" (or from "Yachdav"), that one should not answer 'Amen' louder than the person reciting the Berachah.

(c) From "Moshe Yedaber, ve'ha'Elokim Ya'anenu ve'Kol" we learn that the translator should not raise his voice to speak louder than the reader - from the fact that Hashem, who was only speaking to Moshe, nevertheless raised His voice, to enable Moshe to raise his voice to its fullest extent, to enable the whole of Klal Yisrael to hear him (Tosfos d.h. 'be'Kolo')

(d) If the speaker knows that the translator will be unable to match his voice, then he should lower his own voice.

(a) Our Mishnah obligates three to Bensch Mezuman, the Machlokes Amora'im concerns a voluntary Mezuman.

(b) If two people are permitted to Bensch Mezuman, then why should three people who ate together not be permitted to Bensch Mezuman, even if one of the group left?

(c) Two people may Bensch voluntarily only when their was no prior obligation. If there *was* (i.e. if three people ate together), then they have an obligation to fulfill that obligation.

(d) The two people are only too pleased, if the Shamash joins them to turn a voluntary Mitzvah into an obligatory, as Chazal have taught us in Bava Kama (38a) 'Gadol Metzuvah ve'Oseh, mi'Mi she'Eino Metzuveh ve'Oseh').

4)

(a) The advantage that a hundred women have over two men, is that they have the numbers - they can fulfill the criterion of the Pasuk (where one says to two - "Gadlu la'Hashem Iti", or "Havu Godel l'Elokeinu"), whereas two people cannot.

(b) A group consisting of women and slaves may not Bensch Mezuman together because of the immoral undertones of such a gathering (and the same applies to slaves and children).

(c) When Rav obligates the third person to participate in the Mezuman, that is because the three ate together, obligating them to Bensch Mezuman together. This does not follow that, if two people ate together, they are forbidden to Bensch a voluntary Mezuman.

(d) Since we already know from a Mishnah in Sucah, that one person is Yotze with another's Berachah (even without answering Amen), because of 'Shomei'a ke'Oneh', why did Rebbi Yochanan need to inform us that one person is Yotze with the other's Bensching, unless it is to tell us that he is only Yotze because of 'Shomei'a ke'Oneh', but not because of Mezuman (which is not considered as one person being Motzi another, but two (or three) people sharing the Birchas ha'Mazon.

(a) The Rebbe in Bavel was Rebbi Yochanan. Consequently, if the Rabbanan came from Eretz Yisrael taught that two people are permitted Bensch Mezuman, this would clash with the opinion of Rebbi Yochanan, which we just quoted.

(b) In fact, the Gemara concludes, the Rabbanan from Eretz Yisrael were quoting, not the opinion of Rebbi Yochanan, but that of Rav, before he left Eretz Yisrael for Bavel.

(c) One person out of a group of ten cannot answer where he is. *He* is obligated to return to the group to answer Mezuman. Why is that? Because it is not respectful for the name of Hashem to answer Mezuman in such a casual way.

(d) According to Rav Ashi, if answering from a distance is permitted from a distance when it comes to three people (when the remaining two do not - because of there small numbers - resemble three), then how much more so by ten, where the remaining nine (due to their large number) could pass for ten!

(a) 'Mitzvah Leichalek' means that two people who ate together should recite the Berachah (both before and after eating), individually.

(b) It does not apply when one of the two is a Talmid-Chacham and the other, in which case, it is better for the former to be Motzi the latter.

(a) One person is obligated to stop eating, in order to answer the two who now want to Bensch. But two do not need to answer the one.

(b) Rav Papa, who together with someone else, stopped eating for Aba Mar his son, who wanted to Bensch a Mezuman, acted 'Lifnim mi'Shuras ha'Din'.

(a) Yehudah bar Mereimar, Mar bar Rav Ashi and Rav Acha mi'Difta did not Bensch Mezuman, because they thought that Mezuman was instituted only so that the most important person should Bensch for all the other participants. But when they all equal (such as they were), then what was the point of Bensching Mezuman. In such a case, we should apply 'Mitzvah lei'Chalek'.

(b) But Mereimar told them that although they had fulfilled the Mitzvah of Birchas ha'Mazon, they had lost out on the Mitzvah of Mezuman.

(c) It was however, too late to Bensch Mezuman then, because 'Ein Zimun Lemafrei'a' - the Mitzvah of Mezuman had disintegrated when they Bensched without it.

(a) Someone who has not himself eaten, answers 'Baruch u'Mevorach (Shemo Tamid le'Olam Va'ed').

(b) Rav Papa was speaking when he heard the participants answering, but not the Mevarech. That is why he just answers Amen - to their response.

(a) One only answers ' Amen', after the Berachah of 'BonehYerushalayim' (and also after the final Berachah of Birchos Keri'as Shema, both in the morning and at night-time - which, like 'Boneh Yerushalayim, concludes a set of Berachos).
It is despicable to answer 'Amen' after other Berachos, which do not conclude a set of Berachos such as these.
('Achar Kol Birchosav' in the one Beraisa means 'at the conclusion of 'all' his Berachos, whereas in the other Beraisa, it means 'at the conclusion of 'each' Berachah that he makes' - the former is praiseworthy, the latter, despicable.

(b) Abaye would say 'Amen' out loud after Boneh Yerushalayim', as a signal for the workers (whom Chazal did not obligate to recite 'ha'Tov ve'ha'Meitiv') to go back to work.
Rav Ashi, on the other hand, would make a point of saying it quietly, so that people should not come to belittle the Berachah of 'ha'Tov ve'ha'Meitiv', thinking that Bensching concludes after 'Boneh ve'Rachamav Yerushalayim Amen'.