Question: Perhaps the day is Shavuos (one to seven)?

Answer: We connect a day with one Ayil (Miluim) with another (Yom ha'Kipurim), not with two Aylim (by Shavuos).

Question: But what of the opinion of R. Elazar b. R. Shimon that Yom ha'Kipurim has two Aylim?!

Answer: Even so, one is an obligation of the day, and one is a Musaf, as opposed to Shavuos where both are Chovas ha'Yom.

Question: Perhaps the day is Rosh ha'Shanah?

Answer #1: We connect the days where the animals come from the pocket of the one offering (Miluim and Yom ha'Kipurim), not where they come from communal coffers (Rosh ha'Shanah).

Question: But what of the opinion that the Miluim came from communal funds?!

The Beraisa teaches that Kach L'cha and Asei L'cha mean from your personal funds.

(R. Yoshiyah): ve'Yikchu Elecha means communal funds.

(R. Yonasan) Kach Lecha and ve'Yikchu Elecha mean communal funds. When it says "Kach L'cha by the Ketores," it does not mean communal funds. Rather, it means that so to speak, Hash-m prefers the personal Ketores of Moshe Rabeinu to that of Bnei Yisrael.

Question: There seem to be contradictory Pesukim regarding the funding source of the Aron?

Answer: When Yisrael does His will, the Aron is credited to them; if not (after the Egel) it is credited to Moshe.

Answer: The dispute pertains to unspecified Kichos (like by the Ketores) and Asiyos (like the Chatzotzros), not by specified Kichos like the Miluim.

The source for personal funds by Miluim is Vayikra 9:3.

The source by Yom ha'Kipurim is Vayikra 16:3.

Answer #2: We connect days with one Chatas and one Olah and not days (Shavuos and Rosh ha'Shanah) where both are Olos.

Answer #3 (Ravina): We connect days where the Avodah is done by the Kohen Gadol (excluding all other days).

Alternate Answer #3: We connect Avodah Techilah.

Question: What is Techilah?

Answer: The first Avodah is done by the Kohen Gadol.

Question: But that is the same as Answer #3?!

Answer: It means the Kohen enters the first time.

(R. Dimi citing R. Yochanan): There is one Perishah (Yom ha'Kipurim- "La'asos Lechaper").

(R. Dimi citing R. Yehoshua b. Levi): There are two Perishos (Parah- "La'asos"; Yom ha'Kipurim- "Lechaper").

Question: But the Mishnah teaches that there are two?!

Answer: It is only a stringency by Parah.

Question: But R. Yochanan learned two Perishos from the Pesukim!?

Answer: That was his Rebbi's opinion, not his own (as we find him elsewhere citing this position as R. Yishmael's).

Question (Resh Lakish of R. Yochanan): It appears that the Perishah before Yom ha'Kipurim is Me'akev, as it is by Miluim!?

And if so... why does our Mishnah speak of Mesaknin a substitute Kohen, it should say Mafrishin!?

And if they both mean the same thing, then why does the Mishnah switch words?

Question: What is Resh Lakish's source?

Answer: Moshe's segregation before going up to Har Sinai.

This is found in Shemos 24:17.

Hash-m calls Moshe on the seventh day.

This establishes a six day segregation before any encounter with the Shechinah.

Question: But our Mishnah teaches seven days?!

Answer: Our Mishnah is the opinion of R. Yehudah b. Beseira who reckons with the possibility of Tum'as Beiso.