Resolution #1 (Rav Chama bar Ukva): A visitor [who does not have his own wood] burns in front of the Mikdash using Etzei ha'Ma'arachah; a resident [of Yerushalayim] burns in his Chatzer using his own wood. (Both Mishnayos discuss one who started a journey - we explain like Tosfos.)

Resolution #2 (Rav Papa): Both of them discuss visitors - one who already started a journey [and passed Tzofim] need not return to the Mikdash, one who did not start a journey must return.

Resolution #3 (Rav Zevid): Really, that Mishnah discusses a resident, and our Mishnah discusses a visitor - since a visitor does not have wood, even if he did not start a journey Chachamim apply to him the law of a stingy person:

(Mishnah): Stingy people burn it in front of the Mikdash in order to benefit from Etzei ha'Ma'arachah.

(Beraisa): If one wants to burn it in his Chatzer using Etzei ha'Ma'arachah, we do not accede; if one wants to burn it in front of the Mikdash using his own wood, we do not accede.

Question: We understand why one may not burn it in his Chatzer from Etzei ha'Ma'arachah - we are concerned lest some wood will be left over, and he will transgress [by benefiting from it];

But why can't one burn it in front of the Mikdash using his own wood?

Answer #1 (Rav Yosef): This is to spare from embarrassment one who does not have wood.

Answer #2 (Rava): It is to avoid suspicion [lest others see one take back [his leftover] wood, and they will think that he takes Hekdesh wood].

Question: What is the difference between these answers?

Answer: If someone brought reeds and palm branches, it is known that these are not used for the Ma'arachah [but sparing from embarrassment applies].

(Mishnah): The head of the Ma'amad (Sheluchim of Yisrael to be present at Hakravas Korbanos Tzibur; Rosh (Tamid 33A) the head of the subdivision of Kohanim whose turn it was to work that day) would gather Teme'im (Kohanim) in the eastern gate.

Question: What is the reason?

Answer #1 (Rav Yosef): This was to shame them, so they would be more careful in the future.

Answer #2 (Rava): This is so people will not suspect that they did not want [to desist from their jobs] to serve in the Mikdash.

Question: What is the difference between these answers?

Answers: If a Kohen is very delicate (he detests work) or twines ropes (a paltry, low paying job, surely he does not desist in order to work), there is no suspicion.

(Mishnah): If a Pesach was Yotzei (left Yerushalayim) or became Tamei, it is burned immediately;

If the owners became Tamei or died, it is burned after Ibur Tzurah, on the 16th;

R. Yochanan ben Brokah says, also this is burned immediately, for no one will be able to eat it.

(Gemara) Question: We understand the source that Tamei Kodshim must be burned - "Veha'Basar Asher Yiga b'Chol Tamei Lo Ye'achel ba'Esh Yisaref";

But what is the source that Yotzei must be burned?

Answer: "Hen Lo Huva Es Damah El ha'Kodesh Penimah" - Moshe was asking Aharon why the Chatas [of Rosh Chodesh of Chanukas ha'Mishkan] was burned;

He suggested that perhaps the blood entered the Heichal - Aharon answered that it did not;

Moshe: Perhaps the meat left its Mechitzah (allowed boundary, i.e. Chatzer ha'Mishkan)!

Aharon: No - it was ["Penimah, "] in the Kodesh place (Azarah).

Moshe: If so, you should have eaten it!

Inference: Had the blood entered the Heichal, or had the meat left its Mechitzah, it should be burned.

Question #1: We understand regarding Tum'ah - the Torah requires burning Tamei Kodshim Kalim, all the more so Tamei Kodshei Kodoshim must be burned;

But regarding Yotzei, the Torah requires burning regarding Kodshei Kodoshim - what is the source for Kodshim Kalim?

Question #2: A Beraisa teaches that if the blood spilled, left the Azarah or was not thrown by sunset, the meat must be burned - what is the source of this?

Answer to both questions: We learn like R. Shimon:

(Beraisa - R. Shimon): "Ba'Kodesh...ba'Esh Tisaref" - this teaches that a [Pasul] Chatas is burned in the Kodesh (the Azarah).

Question: What is the source for other Kodshei Kodoshim and Eimurim of Kodshim Kalim?

Answer #1: "V'Chol...ba'Kodesh...ba'Esh Tisaref."

Objection: This teaches about Kodshei Kodoshim - but what is the source for [meat of] Kodshim Kalim?

Answer #2: Rather, we have a tradition that all Pasul Kodshim are burned, be they Kodshim Kalim or Kodshei Kodoshim;

We do not learn Halachos from Aharon's answer to Moshe - the Torah merely records the episode.

Question: Tana d'vei Rabah bar Avuha says that even Pigul requires Ibur Tzurah - what is his source?

Answer: He learns from a Gezerah Shavah "Avon-Avon" from Nosar.

Question: Why doesn't he learn the Gezerah Shavah "Avon-Avon" from the Chatas of Chanukas ha'Mishkan [which was burned that same day]? (See note 48 in Appendix.)

Answer: He holds that normally, it should have required Ibur Tzurah - it was a Hora'as Sha'ah (a special temporary ruling) to burn it the same day.

Question: If a tradition teaches that all Pasul Kodshim are burned, what do we learn from "Ba'Kodesh...ba'Esh Tisaref?"

Answer: It teaches that they must be burned in the Azarah.

Question: What do we learn from "Veha'Basar Asher Yiga b'Chol Tamei Lo Ye'achel ba'Esh Yisaref?"

Answer: That is needed for its simple meaning [that Tamei Kodshim must be burned]:

One might have thought that only Pesulim which do not apply to Chulin must be burned, such as if the blood was left past sunset, spilled or left the Azarah, or if it was slaughtered at night;

But since Tum'ah applies to Chulin, perhaps now that something profane was done to it, it suffices to bury it - the verse teaches that this is not so.

(Mishnah): If the owners became Tamei or died, it is burned after Ibur Tzurah...

(Rav Yosef): They (R. Yochanan ben Brokah, who says that it is burned immediately, and Chachamim) argue in a case when they became Tamei after Zerikah - but if they became Tamei before Zerikah, since the meat was never fitting to eat all agree that it is burned immediately.

Objection (Beraisa): The general rule is - any Pesul ha'Guf is burned immediately; if it is Pasul on account of the blood or the owners, it is burned in Beis ha'Sereifah after Ibur Tzurah.

Surely, the Pesul on account of [Tum'ah of] the owners resembles that of the blood, i.e. it was before Zerikah!

Correction: Rather, Rav Yosef taught that they argue in a case when they became Tamei before Zerikah, since the meat was never fitting to eat, [Chachamim say that] it is like Pesul ha'Guf - but if they became Tamei after Zerikah, since the meat was once fitting to eat, it is like a Pesul on account of something else, all agree that it is burned after Ibur Tzurah.

(R. Yochanan): They argue in both cases.

This is like R. Yochanan taught elsewhere:

(R. Yochanan): R. Yochanan ben Brokah (here) and R. Nechemyah taught the same principle.

(Beraisa - R. Nechemyah): The goat was burned on account of Aninus (after Nadav and Avihu died, Aharon and his remaining sons were Onenim, hence there was no Kohen that could eat Kodshim), therefore it says "[Va'Tikrenah Osi] Ka'Eleh" (it was burned on account of what happened to me; Rashi - even had I suffered a greater loss, I would not have allowed it to become Pasul);

Aninus is like a Pesul after Zerikah (Aharon was Zorek - even if he was already an Onen, a Kohen Gadol Onen is Kosher for Avodah), yet it was burned immediately! (This shows that R. Yochanan holds that R. Yochanan ben Brokah allows burning immediately a Pesul after Zerikah.)