(Continuation of Beraisa): Regarding all Matanos, the giver has Tovas Hana'ah (like we now explain):

If a Yisrael separated Terumah, and Reuven (another Yisrael) offered him some money on condition that he will give the Terumah to a particular Kohen, e.g. Reuven's grandson, this is permitted.

A Kohen (Shimon) may not make such an offer to a Yisrael. (Since the Matanos could be given to Shimon himself, this resembles a Kohen helping in the granary.)

Question: Why does the Tana illustrate only Terumah?

Answer: Terumah has Kedushas ha'Guf (intrinsic Kedushah). The Kohen will not err to think that it became Chulin through a redemptive "sale";

Bechor (Ba'al Mum) and Zero'a, Lechayayim and Kevah are Kedushas Damim (only its value has Kedushah). The Kohen might think that they became Chulin through this "sale" (Rashi - and he will not eat them with the proper grandeur; R. Gershom - he might feed them to dogs.)

(Rava): We are not concerned about a Kohen helping in the granary regarding Terumah of Chutz la'Aretz (which is mid'Rabanan).

Rav Chama would give it to his servant (in lieu of wages).

(Shmuel): Terumas Chutz la'Aretz is Batel in a simple majority of Chulin. (Tosfos - a Tamei Kohen may eat it, but a Zar may not, unless there is 100 times as much Chulin as Terumah. Rashi - it is permitted even to Zarim.)

Rabah (a Kohen) would Mevatel it (in a majority of Chulin), and eat it when he was Tamei.

When Rav Huna brei d'Rav Yehoshua received Terumah wine (of Chutz la'Aretz), he would Mevatel one ladle-full in two ladles of Chulin, (and remove one ladle from the mixture and treat it like Chulin; the Rambam's text omits this);

From then on, he would (always consider the two (Rambam - three) remaining ladles to be Chulin, and) mix in a ladle (of Terumah, to Mevatel it,) and remove a ladle (and treat it like Chulin).

(Shmuel): One may eat Tevel of Chutz la'Aretz, and leave over (Tosfos - a bit more than) the amount needed for Terumah and later designate (Tosfos - from) the remainder to be Terumah.

(Shmuel): A Tamei Kohen may eat Terumas Chutz la'Aretz, unless the Tum'ah comes from the Kohen's own body (e.g. a Zav or Nidah);

Even such Teme'im are forbidden only to eat it, but they may touch it.

(Ravina): Therefore, a Nidah may separate Chalah for a young Kohen to eat. (A boy under nine cannot have an emission. Some permit also an adult Kohen who immersed after his last emission);

If no young Kohen is around, she takes it with a rod (used to stoke coals) and burns it. (Rashi - after calling it Chalah, we minimize its contact with Tum'ah. Tosfos - she uses the rod to put it amidst the coals. Alternatively, she burns it right after removing it from the wall of the oven);

She then separates a second Chalah, and gives it to any adult Kohen to eat. This is so people will not forget the (primary) Mitzvah of Chalah.

Rav Nachman, Rav Amram and Rami bar Chama were on a ship. Rav Amram went to relieve himself. A woman came and asked if one may eat Terumas Chutz la'Aretz after immersing from Tum'as Mes, before nightfall.

Rav Nachman: We do not have Mei Chatas nowadays (in Bavel. Rashi - therefore he need not wait until night; Tosfos - he does not even need Tevilah.)

Rami bar Chama: You should wait until Rav Amram returns before ruling!

Rav Amram returned.

(Rav Amram citing Rav): A Tamei Mes may immerse and eat Terumas Chutz la'Aretz immediately.

The Halachah is not like Rav. (Tosfos - he need not immerse. Rashi - he must immerse and wait until night.)

(Mar Zutra): One who becomes Tamei through a Sheretz may immerse and eat Terumas Chutz la'Aretz immediately.

The Halachah is not like Mar Zutra.

(Mishnah): A Bechor is eaten within the year...

Inference: The Mishnah continues "if it developed a Mum within its year... " This implies that we consider a year from its birth (as opposed to a calendar year, from Tishrei until Elul).

Question: What is the source of this?

Answer #1 (Rav): "Lifnei Hash-m Elokecha Sochalenu Shanah v'Shanah";

Question: What year enters another year?

Answer: The year from its birth enters the next calendar year, from Tishrei until Elul.

(Bei Rav (Shitah Mekubetzes - Bei Rebbi) - Beraisa): "Shanah v'Shanah" teaches that one day in a year is considered a year;

This teaches that a Bechor (offered in the Mikdash) is eaten for two days and a night. (It can be offered on the last day of its year, and eaten on that day and the morrow, which begins its second year.)

Question: What is the source of (the Tana cited by) Bei Rav that we consider its year?

Answer: They learn from other Kodshim.

Question: What is the source for other Kodshim?

Answer (Rav Acha bar Yakov): "Keves ben Shenaso" teaches that we are concerned for its year, and not the calendar year.