1) THE SOURCE THAT THE LOAVES OF "LACHMEI TODAH" MUST BE COMPRISED OF AN "ISARON"
QUESTION: The Gemara derives from the word "Tavi'u" -- "you shall bring" (Vayikra 23:17), written with regard to the Shtei ha'Lechem, that other offerings should be similar to the Shtei ha'Lechem. Just as the Shtei ha'Lechem should have an Isaron for each Chalah, other similar Korbanos should have an Isaron for each Chalah. RASHI (DH Hainu) explains that although the Torah specifies that the Lachmei Todah should have ten Chalos of each type of Chalah, it does not mention how much flour should be used for each Chalah. The Gemara therefore teaches that the ten Chalos of the Lachmei Todah, which are loaves of Chametz, should be compared to the Shtei ha'Lechem, which are also Chametz. Just as each loaf of the Shtei ha'Lechem is comprised of an Isaron, each loaf of the Chalos Chametz of a Korban Todah should be comprised of an Isaron.
What is the source that the loaves of the Lachmei Todah that are not Chametz also must be comprised of an Isaron? The Gemara derives this from the verse, "Al Chalos Lechem Chametz Yakriv Korbano" -- "with loaves of bread that is Chametz he shall bring his Korban" (Vayikra 7:13). Since the previous verse mentions the three types of Chalos of the Todah which are not Chametz, and the Torah then states that that they are brought along with the Chalos which are Chametz, the Torah is teaching that just as the Chalos of Chametz are comprised of an Isaron, the Chalos of Matzah are also comprised of an Isaron. Rashi adds (DH Lamadnu) that the source that there are ten Chalos of Chametz for the Korban Todah is a Gezeirah Shavah from Terumas Ma'aser.
TOSFOS (DH Hainu) asks that if a Gezeirah Shavah from Terumas Ma'aser teaches that there are ten Chalos of Chametz, then how a Hekesh be used to compare the ten Chalos of Matzah to the ten Chalos of Chametz? In order to make a Hekesh from the ten Chalos of Chametz, the Torah must mention the ten Chalos of Chametz explicitly. How can the Gemara learn laws of the ten Chalos of Matzah from the laws of the ten Chalos of Chametz which are not mentioned explicitly?
(a) TOSFOS answers that in this case the Gemara maintains that something derived from a Gezeirah Shavah may then be used to teach something else through a Hekesh. The CHOK NASAN explains that although the Gemara earlier (50a) does not resolve the question of whether a Gezeirah Shavah and a Hekesh may be used in this way, Tosfos understands, for some reason, that they may be used in this way.
(b) Alternatively, Tosfos answers that although a law derived through a Gezeirah Shavah may not be derived to something else through a Hekesh, this applies only when the Gezeirah Shavah is learned from Kodshim. Terumas Ma'aser, however, is considered Chulin, and therefore the Gemara may learn a law from Terumas Ma'aser to Chalos of Chametz through a Gezeirah Shavah, and then from Chalos of Chametz to Chalos of Matzah through a Hekesh.
(c) In his third answer, Tosfos points out that some texts of the Gemara in Menachos (77b) understand that the word, "Tiheyenah" -- "they shall be" (Vayikra 23:17), contains an extra letter Yud. This extra letter teaches that there should be ten Chalos of each of the loaves of the Lachmei Todah. (See Tosfos to Menachos 78a, DH Amar Rav Yitzchak, with regard to reconciling the teaching from the word "Tiheyenah" with the Gezeirah Shavah from Terumas Ma'aser.) (Y. MONTROSE)
2) HALACHAH: BY WHAT TIME MUST ONE EAT THE "AFIKOMAN" ON PESACH NIGHT?
OPINIONS: The Gemara concludes that the Mishnah follows the view of Rebbi Elazar ben Azaryah, who maintains that the Korban Pesach may be eaten only until Chatzos, midnight. This is in contrast to the opinion of Rebbi Akiva, who maintains that the Korban Pesach may be eaten the entire night. In Pesachim (120a), Rava states that one who eats Matzah after Chatzos nowadays (when there is no Beis ha'Mikdash and no Korban Pesach) does not fulfill the Mitzvah of eating Matzah. Rebbi Eliezer ben Azaryah's opinion applies not only to the Mitzvah to eat Matzah but also to the Mitzvah d'Rabanan to eat the Afikoman, which is eaten in commemoration of the Korban Pesach. What is the Halachah in practice?
(a) TOSFOS (DH v'Iba'is Eima) writes that the Halachah follows the view of Rebbi Elazar ben Azaryah. Since Rebbi recorded three Mishnayos in accordance with the view of Rebbi Elazar ben Azaryah (the Mishnah here, the Mishnah in Pesachim 120b, and the first Mishnah in Berachos, as explained by the Gemara in Berachos 9a), and did not even mention the opinion of Rebbi Akiva, presumably the Halachah follows his opinion. Tosfos adds that for this reason, people must be careful to eat the Matzah before Chatzos, in accordance with the statement of Rava in Pesachim (120b, as mentioned above). This is also the opinion of the SEMAG in the name of the RI, the OR ZARU'A, RABEINU CHANANEL and the MORDECHAI in Pesachim, and others.
(b) The RAMBAM, BA'AL HA'ITUR, the RI MI'KORVIL (cited by the Or Zaru'a) and others rule like Rebbi Akiva, based primarily on the Gemara's rule that "Halachah k'Rebbi Akiva me'Chaveiro" -- "the Halachah is like Rebbi Akiva over his colleague" (but not over his colleagues, when more than one Tana argues with him). Since only one Tana argues with Rebbi Akiva in this case, the Halachah should follow the view of Rebbi Akiva.
In addition, the Mishnah in Megilah (20b) implies that the Halachah follows the view of Rebbi Akiva. The Mishnah there says that "any Mitzvah which is supposed to be done at night, may be done the entire night." The Gemara there (21a) explains that the Mishnah's intent is to teach that the Halachah follows the view of Rebbi Akiva, and not the view of Rebbi Elazar ben Azaryah.
However, the LIKUTEI HALACHOS points out that the other Rishonim, such as Tosfos, understand that since the Mishnah here and in Pesachim -- which are the primary Mishnayos that deal with the subject of the Korban Pesach -- follow the view of Rebbi Elazar Ben Azaryah, the Halachah follows those Mishnayos and not the Mishnah in Megilah, which discusses the general issue of the time at which one should perform Mitzvos done at night.
(c) A number of Rishonim, such as the ROKE'ACH, ROSH, RASHBA, and RAN, are in doubt about the Halachah. Therefore, they rule that, out of doubt, one should be stringent and eat the Matzah before Chatzos.
The KESAV SOFER (in his Hagadah) answers an apparent contradiction in the SHULCHAN ARUCH. The Shulchan Aruch rules (OC 477:1) that one should be careful to eat the Afikoman before Chatzos. However, the Shulchan Aruch also rules (OC 481:2) that one is obligated to delve into the Halachos of Korban Pesach and discuss Yetzi'as Mitzrayim "until he is overcome by sleep." The Kesav Sofer points out that the Mitzvah of Sipur Yetzi'as Mitzrayim applies only "b'Sha'ah she'Yesh Matzah u'Maror Munachim Lefanecha" -- "at a time when Matzah and Maror are placed before you." This means that the time to fulfill the Mitzvah of Sipur Yetzi'as Mitzrayim is the same time at which there is a Mitzvah to eat Matzah and Maror. Accordingly, once Chatzos has arrived, there should be no Mitzvah of Sipur Yetzi'as Mitzrayim according to Rebbi Elazar ben Azaryah. Since the Shulchan Aruch rules like Rebbi Elazar ben Azaryah earlier (OC 477:1), why does he not write (OC 481:2) that a person should discuss Yetzi'as Mitzrayim "until Chatzos or until he is overcome by sleep"?
The Kesav Sofer answers that it must be that the Shulchan Aruch follows the view of the Rishonim who are in doubt about whom the Halachah follows, and therefore he rules stringently that the Matzah must be eaten before Chatzos (like Rebbi Elazar ben Azaryah) and that Sipur Yetzi'as Mitzrayim should continue throughout the night (like Rebbi Akiva).
(d) The BI'UR HA'GRA understands that Rebbi Akiva agrees that one is forbidden l'Chatchilah to delay the Mitzvah of eating Matzah until after Chatzos. Accordingly, everyone agrees that one should eat the Matzah before Chatzos, l'Chatchilah. This is also the conclusion of the Likutei Halachos here. (See also BI'UR HALACHAH OC 477 DH v'Yehei Zahir.)
(e) Many people rely on the suggestion of the AVNEI NEZER (OC 381), who proposed a way to circumvent the doubt about when one must finish eating the Afikoman. This is known as the "Tenai of the Avnei Nezer." How exactly to make this condition, and whether or not it works, is the subject of much discussion among the Poskim. (Y. MONTROSE)