Halel and Simcha - rejoicing (eating the meat of a Shelamim sacrifice) are observed for eight days (which includes Shemini Atzeres). How is this?

This teaches that one is obligated to honor the last day of the festival like the rest of the days.

The Mitzvah of Sukah is for seven days. How is this?

When he finishes eating (on the 7th day of Sukos), he should not disassemble his Sukah. Rather, from Minchah-time onwards, he should remove his vessels from the Sukah, in order to show honor to the Yom Tov that will be occurring that evening.

Beraisa: There are 18 days and one night every year on which we recite [full] Halel - the 8 days of Sukos, the 8 days of Chanukah, on Shavuos (1 day), on the 1st day and on the 1st night of Pesach.

R. Zeira/ Ula bar Shmuel quoting R. Elazar: If a person slaughtered the Shalmei Chagigah offering before the onset of the festival, he does not fulfill his obligation on the festival.

Question (R. Ba - Beraisa): The Chagigah of the 14th - one may fulfill with it his obligation of Simchah but not his obligation of the Shelamim offering.

Answer (R. Zeira): In this case, he slaughtered it during the festival itself.

Question (R. Ba): If he slaughtered it during the festival, it is not the Chagigah of the 14th! Could he fulfill his obligation of Shalmei Chagigah with it?

Answer: R. Zeira said that he heard the explanation in Bavel; Ula bar Yishmael quoting R. Elazar said that he heard it when he came here to Eretz Yisrael -

R. Chiya quoting R. Elazar: The Pasuk states (Devarim 16, 15), "And you shall be (Ach) only happy". This includes the last night of the festival in the Mitzvah of Simchah. But perhaps it also includes the first night of the festival? The Pasuk says "Ach" - "only" - this splits the law.

R. Chiya quoting R. Elazar: The Pasuk states (Devarim 16, 14), "And you shall rejoice on your festival" - from when you are obligated in the Chagigah, you are obligated in Simchah.

Question (Mishnah): Halel and Simchah are observed for eight days.

If the first day occurs on Shabbos - you cannot slaughter them before the festival as R. Zeira/ Ula bar Yishmael quoting R. Elazar said that if one slaughtered the Shalmei Chagigah before the festival, he has not fulfilled his obligation on the festival.

You cannot slaughter them on the festival as the Chagigah does not override Shabbos.

Question: When did they say that Halel and Simchah are observed for 8 days? (If the 1st day occurs on a weekday, the Mishnah should teach that Simchah is observed for seven or eight days, as it did for Lulav and Aravah)?

Answer (R. Yosa): Rav Avudimi, who would often travel from Eretz Yisrael to Bavel, said that it refers to Kohanim who eat the Chatas (of the festival Musaf offering) which is a goat. (Its sacrifice overrides Shabbos and the Kohanim eat it raw.)

R. Aba bar Kahana/ R. Chiya bar Ashi quoting Rav: One must invalidate his Sukah before the onset of the last day of Yom Tov.

R. Yehoshua ben Levi: He should merely recite Kidush (that night) in his home. (This is enough to indicate that he does not wish to extend the Mitzvah of Sukah.)

R. Yaakov bar Acha quoting Shmuel: (On a regular Shabbos or Yom Tov) if a person recited Kidush in one house and decided to eat in another house, he must recite Kidush again (as he did not eat his meal in the place that he had recited Kidush).

R. Acha/ R. Chinana/ Rav Hoshiya quoting Rav: If a person enjoys being in his Sukah, he may recite Kidush in his home on the last night of Yom Tov and then proceed to eat in his Sukah.

R. Avin: They do not disagree ((c) and (d)) - Rav was referring to when he was not intending to eat in the original house (so he does not need to recite Kidush again, as he intended to eat in the Sukah); Shmuel was referring to when he recited Kidush intending to eat there (so when he goes elsewhere, he must repeat Kidush).

R. Mana: Shmuel follows R. Chiya [bar Ashi quoting Rav, who appeared earlier (a)] and R. Hoshiya follows R. Yehoshua ben Levi (see (b)).