WHAT MAKES THE TENTH KODESH
(R. Elazar ben Gomel): It says "v'Nechshav Lachem Terumaschem (ka'Dagan Min ha'Goren)." Terumaschem refers to (and equates) two Terumos, i.e. Terumah Gedolah and Terumas Ma'aser;
Just like Terumah Gedolah is taken by estimation and may be designated with mere intent (without an action or words), also Terumas Ma'aser;
Ma'aser (of grain) is called Terumah - "Ki Es Ma'asar Bnei Yisrael Asher Yarimu la'Shem Terumah Nasati la'Leviyim."
Just like Ma'aser of grain is taken by estimation and with mere intent, also Ma'aser Behemah (Rashi Kesav Yad - can be taken without counting).
(Rava): The tenth is Kodesh automatically (even if he did not call it Asiri. Alternatively, it is Kodesh even if it did not leave the pen.)
Question: What is his source?
Answer #1 (Beraisa) Question: Perhaps this is only if he called it "Asiri". What is the source to include if he did not do so?
Answer: "Yihyeh Kodesh" in any case.
Rejection: Perhaps the case is, he did not call it "Asiri," but called it "Kodesh". (Alternatively, perhaps it is Kodesh to forbid eating it without a Mum, but it is not offered.)
Answer #2 (Beraisa): If he (mistakenly) called the ninth "Asiri," and was silent when the tenth left, the ninth is eaten when it gets a Mum, and the tenth is Ma'aser.
Rejection #1: Perhaps that is different, for the tenth did leave.
Rejection #2: Perhaps the case is, he pointed to show that it is the tenth.
Answer #3 (Beraisa): If he called the ninth "Asiri," and the tenth died in the pen, the ninth is eaten when it gets a Mum, and the first eight are exempt from Ma'aser.
Suggestion: The first eight are exempt because the tenth became Ma'aser!
Rejection: No, Minyan ha'Ra'uy (when they left, the pen contained enough to complete the count of 10) exempted them;
(Rava): Minyan ha'Ra'uy exempts.
Answer #4 (Beraisa #1): If he called the ninth "Asiri," and the tenth remained in the pen, the ninth is eaten when it gets a Mum, and the tenth is Ma'aser.
Contradiction (Beraisa #2): The ninth is Chulin. (It may be eaten immediately.)
Answer (a reciter of Beraisos): Beraisa #2 is like R. Shimon;
(Beraisa - R. Shimon): The ninth is not Kodesh unless (the name of) the tenth was Ne'ekar (it was called something else, e.g. ninth).
A Kal va'Chomer supports this. The 11th gets Kedushas Hakravah (it is offered like a Shelamim if it was called tenth), but only if the tenth was Ne'ekar. The Kedushah of the ninth is not for Hakravah (rather, just to forbid it without a Mum), all the more so this is only if the tenth was Ne'ekar!
Rejection #1: Just the contrary! Because the Kedushah of the 11th is for Hakravah, this is only if the tenth was Ne'ekar. The Kedushah of the ninth is not for Hakravah, so this can happen even if the tenth was not Ne'ekar! (Rashi attributes these rejections to the Gemara. Rashi Kesav Yad attributes them to Chachamim.)
Rejection #2: Because the tenth was determined before the 11th, the 11th gets Kedushah only if the tenth was Ne'ekar. (If not, the 11th is like the first of the next 10. Calling it Asiri has no effect.) However, the ninth was called Asiri before the tenth was determined. This can happen even if the tenth will not be Ne'ekar!
MINYAN HA'RA'UY EXEMPTS
(Rava): Minyan ha'Ra'uy exempts.
Question: What is his source?
Answer #1 (Mishnah): If one of the counted animals re-entered the pen, they are all exempt.
Suggestion: The counted animals were exempt through Minyan ha'Ra'uy!
Objection: Perhaps they are exempt because Ma'aser was taken! (However, if all 10 did not leave, they are not exempt.)
Rejection: This cannot be, for the Seifa discusses that!
(Seifa): If one of the tithed animals re-entered the pen...
Objection: Perhaps the Seifa means that the Asiri re-entered the pen!
Support: It says that each is Ro'eh, and the owner eats it when it gets a Mum. Surely, the Asiri entered the pen.
Answer #2 (Rava): "Ya'avor" excludes an animal that already left before.
Question: What is the meaning of 'that already left before'?
If it was part of 10 that left and Ma'aser was taken, we do not need a verse for this!
Answer: It was exempted through Minyan ha'Ra'uy.
Support (Beraisa): If Reuven had 10 lambs and brought them into a pen, and counted five and one died:
If one of the counted ones died, he completes the count for Ma'aser (as if all were alive);
If one of the remaining ones died, the counted ones are exempt (due to Minyan ha'Ra'uy). The remaining ones will join for Ma'aser in the next Goren.
(Rava): If Reuven had 14 lambs, and brought them into a pen with two openings:
If six left from opening 1 and then four left from opening 2, and four remained;
If the last four leave from opening 1, the last is Ma'aser. The four that left from opening 2 will join (for Ma'aser) in the next Goren.
If not (they leave from opening 2 or remain in the pen), the six are exempt (Minyan ha'Ra'uy), and the other eight join in the next Goren.
If four left from opening 1 and then six left from opening 2, and four remained;
If the last four leave from opening 2, the last is Ma'aser. The four that left from 1 are (also) exempt;
If not, the first 10 that left are exempt, and the last four join in the next Goren.
If four left from opening 1 and then four left from opening 2, and six remained;
If the last six all leave from opening 1 or all from 2, the last is Ma'aser, and (also) the four that left from the other opening are exempt;
If not (they leave from a third opening or remain in the pen), the first eight are exempt, and the six join in the next Goren.
Question: Presumably, the Chidush is that Minyan ha'Ra'uy exempts. Rava already taught this!
Answer: One might have thought that only a definite Minyan ha'Ra'uy (when there is only one opening, we expect all 10 to leave through it) exempts, but not a Safek Minyan ha'Ra'uy. Rava teaches that this is not so. (Alternatively - it is called Safek Minyan ha'Ra'uy when the same set of animals remaining in the pen exempts two sets of animals that left through different openings.)