R. Nachman reported his source that the Payis is done in Bigdei Chol.

The Mishnah teaches that the attendants removed all but the Michnasayim of the Kohanim.

We assume that these Kohanim are the ones who won.

The changing, then, is into Bigdei Kodesh, from Bigdei Chol!

(R. Sheishes): No, the attendants removed the garments of those who lost.

This is supported by the fact that they left on the Michnasayim, which must be the first garments to be donned.

If we were speaking of the winning Kohanim, then the Michnasayim would then be donned last.

(R. Nachman): No, the attendants put Michnesei Kodesh on the winners first, then removed the rest of their Bigdei Chol, leaving them with Michnasayim.

R. Sheishes reported his source that the Payis is done in Bigdei Kodesh.

The Beraisa teaches that the overseer of the lottery removed the Mitznefes from the head of the starting Kohen, a garment only appearing in Bigdei Kodesh!

No, there were Kohanim who wore a Mitznefes Chol.

(Abaye): The Lishkas ha'Gazis must have been half in Kodesh and half in Chol.

The sitting elder indicates that there must have been a part in Chol.

The Pasuk "be'Vais Elokim... " indicates that the Payis must have been in Kodesh.

Also, it must have had an entrance to both Kodesh and Chol.

Since its entrance determines the status of the room, it must have had an entrance to Chol, since he sat.

The Payis indicates that it had an entrance to Kodesh.

The Mishnah lists the 13 tasks which the second lottery assigned.

Ben Azai (citing R. Yehoshua) argues over the order in which the parts of the Tamid were brought onto the Kevesh.

Question: Was a Payis conducted for each of the 13 tasks, or was one Payis conducted and the tasks were automatically assigned from that one?

Answer: We have been taught that there were a total of four.

No, that they entered four times for Paysos (but perhaps they had many Paysos once they entered).

From the Beraisa regarding the Ketores and Machtah in the third Payis we see that there were only four, and the other tasks were automatically assigned to the Kohen to his right.

No, that was unique to the Ketores and Machtah (but our 13 would involve separate Paysos).

Alternately, the sequence began with the inference that other Avodos (than Ketores and Machtah) required a separate Payis, since these were singled out

No, they were singled out because we might have (incorrectly) made two Paysos for them.

In the end, a clear Beraisa teaches that the other 12 assignments were automatic after the first Payis.

Question: Is the Shochet also the Mekabel, or is the Zorek?

The Zorek might rush the Kabalah.

The Shochet might be a Zar.

Answer: The 12 spigots of Ben Katin teach us that it is the Zorek who is the Mekabel (R. Acha cites a supporting Beraisa).

The Tana Kama teaches the order of its Hiluch (cited by Ben Azai in the name of R. Yehoshua).

R. Yosi teaches the order of its Hefshet.

R. Akiva teaches the order of the Nituach.

R. Yosi ha'Gelili teaches the order of its Ilui.

Question: But from the Pasuk we learn that the Yerech is more valuable than the Kasef?!

Answer: That speaks of a lean animal.

(Rava): The Tana Kama and R. Yosi ha'Gelili agree regarding the priority of value, and only argue as to whether size (Tana Kama) or fat (R. Yosi ha'Gelili) is valued more.

Question: Why do all the Tanaim agree that the right hind leg goes together with the head.

Answer: It, like the head, has many bones.

Question: What is the source that the head is first?

Answer: The Pasuk puts the Rosh and Pader first to "ve'Arach".

Question: Why does Pader need to be singled out?

Answer: It was placed over the Beis ha'Shechitah for Kavod.