(Beraisa #1): If the tenth and 11th came out together, Ro'eh (each grazes until it gets a Mum, it is then eaten).

Contradiction (Beraisa #2): They are offered.

Contradiction (Beraisa #3): We lock them up and let them starve to death.

Answer - part 1: Beraisa #1 is like Chachamim, who say that Ein Mevi'im Kodshim l'Veis ha'Pesul. (We may not offer Kodshim if they might become Nosar due to a Safek that decreases the time or number of people allowed to eat them. Chazah v'Shok of Ma'aser is permitted to Zarim, and that of Shelamim must be eaten by Kohanim. Since we do not know which is the Shelamim, Chazah v'Shok of both animals must be eaten by Kohanim.)

Answer - part 2: Beraisa #2 is like R. Shimon, who says that Mevi'im Kodshim l'Veis ha'Pesul;

Answer (#1) - part 3: Beraisa #3 is like R. Yehudah, who says that Ta'us Ma'aser is a Temurah;

He holds that Temuras Ma'aser must die.

Objection: This is not true!

(Mishnah - Rabanan citing R. Meir): If the 11th was Temurah, it would not be offered.

(He said this to refute R. Yehudah.) We must say that R. Yehudah agrees that the 11th is offered!

Suggestion: Perhaps R. Meir said "according to my reasoning (that it is offered), it cannot be Temurah."

Rejection #1 (Beraisa - R. Yehudah): The only difference between the 11th and Shelamim is that Shelamim can make (through Temurah another) Kedushah that can be offered, but the 11th cannot make Kedushah that can be offered.

Inference: The 11th cannot make (another) Kedushah that can be offered, but it itself is offered!

Rejection #2: (Beraisa): "Im Min ha'Bakar" includes the 11th. It is a Shelamim.

Suggestion: Perhaps we include even the ninth!

Rejection: Something cannot make Hekdesh (through Temurah) before it itself is Hekdesh, only after it is Hekdesh! (The ninth was called "Asiri" before the tenth became Ma'aser.)

A Stam (anonymous) Sifra (Toras Kohanim, a Beraisa expounding a verse in Vayikra) is assumed to be R. Yehudah, and it says that the 11th is a Shelamim!

Answer (#2) - part 3 (R. Shimon b'Rebbi Aba): Beraisa #3 applies after the Churban. The animals die due to Takalah (if we wait for them to get Mumim, perhaps someone will come to shear or work with or blemish them)!

Question: If so, why does the Tana discuss when two came out together? The same should apply even if they came out one after the other!

Answer: The Mishnah teaches a bigger Chidush:

We decree not only when they came out one after the other, so only one is Kodesh, and it is a small loss. Rather, even when they came out together, we decree that both must die, and one may not graze them (to eat them after they get Mumim).

(Rav Papi): If Reuven made a Shali'ach to take Ma'aser Behemah, and the Shali'ach called the ninth "Asiri," it is Kodesh (this is not a major loss. It will be eaten after it gets a Mum);

If he called the 11th "Asiri," it is not Kodesh. (If it would become a Shelamim, the Chazah v'Shok would be given to Kohanim, which is a loss for the owner. A Shali'ach is made for one's benefit, not for his detriment!)

(Rav Papa): Also the ninth is not Kodesh, for even this is detrimental to Reuven. (He cannot shear it or work with it, and he must wait for it to get a Mum. It might die or become Terefah before this!)

Question: Why is this different than the following Mishnah?

(Mishnah): Reuven's Shali'ach to take Terumah should take the amount that Reuven wants;

If he does not know how much Reuven wants to take, he should take one part in 50, like average people do;

If he took one in 40 or one in 60 (Rambam - thinking that Reuven wants this), it is Terumah. (Even though one in 40 is more than Reuven wanted to give, we do not say that the Shelichus is Batel!)

Answer: Regarding Terumah, some (i.e. generous) people normally take one in 40. The Shali'ach can say 'I thought that this is what you wanted';

Here, the Shali'ach erred.