(R. Simon): (When R. Eliezer said in the Mishnah (Chulin 82-2(e)) that if a Se'ah of Tamei Terumah fell into 100 Se'ah of Tahor Chulin, he should remove a Se'ah and burn it) he follows his reasoning - just as he said there (in Maseches Zevachim 8:5) that according to R. Eliezer, (if limbs of an animal with blemishes became mixed limbs of sacrifices; if one of the heads was already sacrificed, the rest maybe sacrificed) on the assumption that the first one was the blemished one (since strictly speaking, the limbs are annulled in the majority); so too here, we assume that the Se'ah removed was the Terumah that fell (since strictly speaking, the Terumah was annulled in the majority).

Question (R. Zeira): Or perhaps we could say that R. Eliezer said that the Se'ah removed is burned because of a Rabbinic decree to view it as if it is the Terumah that fell, to prevent Kohanim being lenient in eating it since it was annulled in 101 parts...

Proof: Doesn't R. Eliezer agree that if a Se'ah of Terumah fell into 100 Se'ah of Tevel, that he would need to tithe the Se'ah that he removes, since it might be Tevel? But if the same Terumah that fell in came out, why would it need tithing?!

(R. Mana): R. Zeira is correct, as our Mishnah continues to say - 'If a Se'ah of Tahor Terumah fell into 100 Se'ah of Tamei Chulin, he should remove a Se'ah and the Kohen should eat it dry...' R. Eliezer doesn't disagree (but if he would say that the Se'ah that was taken out was certainly the one that fell in, why would it have to be eaten dry?!)

(Chevraya to R. Yosi): R. Simon is correct (that the Se'ah taken out was certainly the one that fell in), as otherwise, would we burn the Terumah because of a Rabbinic decree?

(R. Yosi to Chevraya): The 6 cases of doubt in the Mishnah (in Maseches Taharos 4:5) are Rabbinic decrees and they are still burned! Here too, can't it be burned even though it's a Rabbinic decree?!

Question (Chevraya to R. Yosi): Either way - if it's the Tamei Terumah, it must be burned; and if it's the Chulin, what's wrong with burning it?!

Answer (R. Yosi to Chevraya): Isn't it ruled to be Terumah? Can Tamei Terumah be eaten? Don't you agree that if a doubt of Tumah arose in the Tumah before it fell, that you may not burn it. So what's the difference whether the doubt arose elsewhere (when it fell) or before it fell? (And in either case, it cannot be burned.)

Rather, if you wish to ask, ask on the Baraisa of R. Hoshiya, that taught...

If a Se'ah of Tahor Terumah fell into 100 Se'ah of Tamei Terumah (the Se'ah removed from the mixture must be left to rot. But shouldn't it be burned like Tamei Terumah?) (The Gemara leaves this question unanswered.)

(The Mishnah taught that the Kohen should eat the Se'ah dry...or as small buns.) These small buns should be the size of half a Se'ah.

(Chizkiyah): Even the rest of the Chulin should be eaten in one of these forms, so that Challah can be taken.

We learn from Chizkiyah that the prohibition of a non-Kohen eating it is annulled, but not the Tumah.

Question: The opinion of Chizkiyah seems to have switched - there (in Tosefta Challah - it says that if less than an egg-size of Tamei flour became mixed with Tahor flour; when he comes to separate Challah, he says, "This is Challah, aside from the Tamei part'', thereby allowing the Kohen to eat the Challah and the rest is Chulin and is eaten in Tumah.) - How much Tamei flour and other flour can be in the dough and he can still use in the dough in Taharah? Chizkiyah said - 1/6th of four Kav of Tamei flour and 4 Kav of flour in total - 1/6th of 4 Kav is certainly enough to give Tumah; but here he said that all of the dough must be in Taharah in order to separate Tumah...?

Answer (R. Yosi): There (about our Mishnah), he first made a large dough and then separated Challah, so that if the dough became Tamei, so did the Challah. But here (in the Tosefta in Challah), he separated an amount for Challah and kneaded it separately.

(R. Abahu): We never knew why Chizkiyah said 1/6th of four Kav, until we made the calculation - How many eggs amount are in a Kav? 24. Therefore, in 4 Kav, there are 96 eggs. 1/6th of the flour is therefore 96/6=16 eggs' amount.

If he makes a dough of 6 eggs' amount (of which at least four are Tahor), there would be one egg's amount of Tamei flour; which would spread Tumah throughout the dough. If he makes a dough of 4 eggs' amount, there isn't enough dough to be obligated in Challah. What should be do? Mix 5 eggs (of which 4 are Tahor) and take 4 and declare Challah aside from the Tamei flour. (And since the Tamei is 1/6th and there are only 5 eggs, the Tamei is less than an eggs amount.)

Chizkiyah's teaching relies on being particular that an eggs amount of Tamei flour doesn't touch the separate part (of the kneading bowl).

R. Yochanan's teaching relies on being particular that an eggs amount of Tamei flour doesn't touch the rest of the dough.

Question (R. Yosi to R. Yirmiyah): Isn't it logical that Chizkiyah was referring to when a person had already kneaded the dough in the separate part in Taharah and the rest in Tumah; whereas R. Yochanan was teaching that ideally, all of the dough should be kneaded in Taharah? (And in fact, they do not disagree.)

(R. Yirmiyah to R. Yosi): I agree.

Question: According to R. Yochanan, how much dough could be in the (small) separate dough (so that it could be separated as Challah for the rest of the dough)?

Answer (R. Yona): Where he kneaded dough that is 1/17th of the large dough (of around 5 Se'ah, so that it does not contain an eggs amount of Tamei flour). And since the Challah is 1/24th of the entire dough, it can be the Challah for the first 5 Se'ah plus another dough of 2 Se'ah.

Question (R. Ba bar Mamal): (The Gemara stated earlier (c) that according to Chizkiyah, the prohibition of a non-Kohen eating it is annulled, but not the Tumah.) Doesn't this disagree with R. Yosi bar Chaninah who said that if a piece of (Tamei) carcass (i.e. Neveilah) became mixed with pieces of slaughtered meat (which are the majority), the majority annuls the Tumah status only for the Tumah of touching, but not the Tumah of moving, since slaughtered meat cannot become Neveilah. (This shows that Tumah can be annulled, unlike Chizkiyah.)...?

Answer (R. Yosi): It's impossible for slaughtered meat to become a Neveilah, but the Chulin can contract Tumah like the Terumah.

(R. Chizkiyah): In the previous question, in fact R. Simon was the questioner (rather than R. Ba bar Mamal) and R. Ba bar Mamal gave the answer.

Baraisa: If a Se'ah of Terumah fell into less than 100 Se'ah of Chulin, it is Medumah (a prohibited mixture to non-Kohanim) and he may only pay the principal and extra fifth from the Chulin proportion of the mixture. And this calculation is only made if the mixture was dry with dry, since they don't fully mix; but for liquids that fully mix, it's considered one mixture - so in terms of the payment, if the majority was Terumah, it's viewed as only Terumah (and may not be used) and if the majority was Chulin, it's viewed as only Chulin.