WHICH FIGS ARE MA'ALEH?
Answer #1 (Rav Papa): (R. Yochanan explained the Tana of the Mishnah.) This Tana holds that everything that is normally counted is Mekadesh, even regarding an Isur mid'Rabanan, like the Tana of the following Beraisa:
(Beraisa - R. Meir): If a Litra (a measure) of (Terumah) figs was pressed onto the top of a barrel (or another Kli) and it is not known which barrel:
R. Eliezer says that (even though we know that the Terumah figs are on top), we consider all the figs to be involved in the Safek. If there are at least 101 Litros of figs in the barrels, they are Ma'aleh the Terumah (i.e. they are Mevatel it. We remove one Litra and treat it like Terumah, and the rest is permitted like Chulin. If there are not 101 Litros, all are forbidden like Dimu'a, i.e. a mixture of Terumah and Chulin);
R. Yehoshua says, (since we know that the Terumah is on top) if there are at least 101 tops (i.e. of barrels where the Terumah might be), they are Ma'aleh the Terumah. If not, the tops are forbidden (like Dimu'a), and the rest is permitted.
R. Yehudah says, R. Eliezer says that if there are at least 101 tops, they are Ma'aleh. If not, the tops are forbidden, the rest is permitted;
R. Yehoshua says, even if there are 300 tops, they are not Ma'aleh (for figs are sometimes counted).
If they were pressed into a barrel but it is not known into which part of the barrel, all agree that all the figs combine to be Ma'aleh the Terumah.
WHY MUST ALL THE ANIMALS DIE?
Answer #2 (Rav Ashi): The Beraisa can even be like Chachamim. Living animals are important, so they are not Batel.
Question: Why don't we remove animals from the mixture one by one (until only two remain. The Halachah assumes that) each is from the majority (that are permitted)!
Objection: If we did, the Isur would be considered Kavu'a (fixed in its place). Such cases are considered like an even doubt (we do not follow the majority)!
Question: Rather, let us force them to go away (so animals will separate from the mixture elsewhere, not in front of us). Then, each that separates is (assumed to be) from the majority!
Answer #1 (Rava): Chachamim decreed not to do so, lest simultaneously, each of (e.g.) 10 Kohanim will offer (the blood or Eimurim of) one of the animals, and this will be the majority of the remaining animals (i.e. less than 20 remain. Presumably, the forbidden animal is among them!)
Objection: If (at the time of Shechitah) each was assumed to be (from the majority, i.e.) permitted, it remains permitted!
Answer #2 (Rava): Rather, the concern is that simultaneously, each of 10 Kohanim will take an animal that separated from the mixture in order to offer it (and these 10 will comprise the majority. Presumably the forbidden animal is among them.)
Objection: We could not coordinate that if we wanted to (since we force the animals to go away. Surely, we need not be concerned for it!)
Answer #2 (Rava): Chachamim decreed not to do so, lest someone take in a way (i.e. from the mixture) that is considered Kavu'a.
DOES DICHUY APPLY TO THE MIXTURE?
(Rava): Since Chachamim forbade offering the animals (they are Nidchim, i.e. permanently disqualified;) if any were offered, they are Pesulim.
Question (Rav Huna bar Yehudah - Mishnah): If Chata'os and Olos ha'Of became mixed together, even if one was mixed with 10,000 of the other, all must be left to die;
If (there were equal numbers of Chata'os and Olos, and) a Kohen erred and offered all of them above (like Olas ha'Of), half are Kesherim (the Olos);
If he offered all of them below (like Chatas ha'Of), half are Kesherim;
If he offered half above and half below, all are Pesulim, for perhaps all Olos were offered below and all Chata'os above.
(According to Rava, since it was forbidden to offer them, in all cases all should be Pesulim!)
Answer: Rava's law is like the opinion that a living animal can be Nidcheh. The Mishnah is like the opinion that it cannot.
Question: All agree that a slaughtered animal can be Nidcheh, yet R. Eliezer is Machshir (if one of a mixture was offered)!
(Mishnah - R. Eliezer): (If the limbs of a blemished Olah were mixed with limbs of Kosher Olos,) if one of the heads was offered (we assume that this was the blemished animal), we offer the rest of the heads.
Answer: R. Eliezer holds like Chanan ha'Mitzri (who holds that even slaughtered animals are not Nidchim);
(Beraisa - Chanan ha'Mitzri): If the blood of the goat (to be offered in the Kodesh ha'Kodoshim on Yom Kipur) was collected and the Se'ir ha'Mishtale'ach (the goat sent to Azazel) died, we bring another goat to be the Se'ir ha'Mishtale'ach. The collected blood is still Kosher.