1) WHAT IS THE ORDER OF THE MISHNAH?
QUESTION: The Mishnah says that a group of ten that says Birkas ha'Mazon is no different than a group of ten thousand -- both groups recite the same words. The Mishnah then continues and seems to contradict itself. It specifies different texts that groups of different numbers say. The Gemara explains that the beginning of the Mishnah is the opinion of Rebbi Akiva, and the rest of the Mishnah is the opinion of Rebbi Yosi ha'Glili. Why, though, does the Mishnah not mention their names in connection with their opinions?
ANSWER: The VILNA GA'ON answers that when the Mishnah says that a Zimun of ten and a Zimun of ten thousand are the same, it means that they are the same only insofar as they both mention the name of Hash-m in Birkas ha'Zimun (in contrast to the words that a group of three says, as discussed earlier in the Mishnah). The continuation of the Mishnah describes the additions to Birkas ha'Zimun that larger groups make in addition to the inclusion of the name of Hash-m. Thus, the end of the Mishnah does not contradict the earlier statement at all.
According to this, the entire Mishnah is the opinion of Rebbi Yosi ha'Glili. What, then, is the Gemara's question, and why does it answer that the first part of the Mishnah is the opinion of Rebbi Akiva?
The Vilna Ga'on explains that it is obvious from the second part of the Mishnah that ten is the same as ten thousand with regard to the inclusion of the name of Hash-m. The Gemara's question is why the Mishnah must add the statement that a Zimun of ten and a Zimun of ten thousand are the same (with regard to the inclusion of the name of Hash-m) when that may be inferred from the end of the Mishnah. The Gemara answers that the additional statement in the Mishnah (that ten men and ten thousand men are the same) is alluding to the opinion of Rebbi Akiva, who maintains that they are the same with regard to the entire text they recite and not just with regard to the name of Hash-m. Even though the simple understanding of the Mishnah is that it is teaching us Rebbi Yosi's opinion (and, therefore, the statements in the Mishnah are not out of order), the Mishnah inserts an apparently unnecessary phrase into the opinion of Rebbi Yosi in order to allude to the opinion of Rebbi Akiva, whose opinion is the Halachah.
2) FETUSES IN THE WOMB SANG PRAISE TO HASH-M WHEN THE SEA SPLIT
QUESTION: Rebbi Akiva and Rebbi Meir derive from a verse that even fetuses in the womb sang praise to Hash-m when the Sea split.
Why did the unborn fetuses have to praise Hash-m when the Sea split?
ANSWER: The RASHBA explains that it is common for a woman to miscarry when she experiences an extreme fright. When the Jews faced the oncoming Egyptian army at the Sea, there was great reason to panic and subsequently for women to miscarry. In addition, it was very frightening to walk between the two walls of the divided Sea. Nevertheless, none of the fetuses died. Therefore, it was incumbent upon those unborn children to praise Hash-m for the miracle that happened to them.

50b----------------------------------------50b

3) THREE PEOPLE WHO LEFT THREE GROUPS
OPINIONS: The Gemara says that if three people -- who were part of three separate groups that were obligated to make a Zimun -- left their groups, and their original groups recited Birkas ha'Zimun, these three may no longer make a Zimun even if they come together to form a new group.
The Gemara cites a proof from the Mishnah in Kelim (18:9). The Mishnah there teaches that a bed that was Tamei and was broken and then re-assembled is not Tamei when it is re-assembled.
There are several ways to understand this Gemara. Two of the approaches are as follows:
(a) TOSFOS RABEINU YEHUDAH HA'CHASID explains that Rava is teaching that if the three deserters were originally in groups of four people, then if -- after they left their groups -- the remaining three in each group made a Zimun, the deserters can no longer make a Zimun based on the meal that they ate earlier. (Even though they were obligated to make a Zimun and they did not yet participate in a Zimun, they forfeited their opportunity to do so).
(b) The ROSH (7:29) does not accept this explanation, because the phrase, "Azmin Alaihu" ("they made a Zimun with them") implies that the deserters actually participated in the Zimun. Therefore, the Rosh explains that if the deserters participated in the Zimun by responding to it before they left their original groups, they may no longer join with each other to form a Zimun when they want to recite Birkas ha'Mazon. This is the opinion of RASHI (DH Aval) and TOSFOS (50a, DH Aval) as well.
This explanation is problematic, though, because it is obvious that they cannot form a new Zimun if they already participated in one! The Rishonim offer two approaches to resolve this problem.
1. The Rosh himself explains that even if they eat more food together afterwards, they still may not make a Zimun because they did not start a new meal together, but they merely continued their old meal which was already exempt from Zimun.
2. The RA'AVAD cited by the RASHBA explains that even if the deserters wanted to leave their original groups before those groups made a Zimun, if the original groups coerced them to join their Zimun before they had a chance to run out, they are exempt from the obligation of Zimun and may no longer make a Zimun with others whom they join later. (The Ra'avad is one of the Rishonim who rule that it is not necessary for the third member of the Zimun to actually respond; he must just be present. See Insights to Berachos 45:3.)
HALACHAH: The SHULCHAN ARUCH (OC 193:5) cites the opinion of the Rosh that if three people were part of three separate groups that were obligated to make a Zimun, and they left their original groups and joined each other and ate more, they cannot make a Zimun if the original groups made a Zimun already. However, the BI'UR HALACHAH says that it is not clear what the Halachah would be in a case in which only one of the people in the second Zimun was a deserter (while the other two had begun their meal together, and had not responded to a Zimun). Perhaps if they were to eat more together they would indeed be obligated in their own Zimun. The Halachah in such a case remains unresolved.

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