Gemara

13b - Mishnah: If rice, millet, poppy or sesame took root before Rosh Hashanah, it is tithed like last year's produce, and it is exempt from Shemitah (if the coming year is Shemitah);

If not, it is forbidden in Shemitah (if the coming year is Shemitah, and if not) it is tithed like the coming year's produce.

Question (Rabah): Chachamim said that we follow Chanatah regarding trees, a third growth regarding Tevu'ah, and picking regarding Yerakos. Like which do Chachamim consider rice,...?

Answer (Rabah): Since they are picked a bit at a time, Chachamim follow Hashrashah (when they took root. If we followed picking, one might tithe from old on new or vice-versa).

Question (Abaye): Chachamim could say that when tithing one must mix all the produce together (uniformly), so he will tithe from Chodosh (this year's produce) on Chodosh and from Yashan (last year's produce) on Yashan (like a Beraisa permits)!

Beraisa - R. Shimon Shezuri: If Mitzri beans were planted for the sake of their seeds (they are considered like legumes, Ma'aser is taken according to Hashrashah), and some took root before Rosh Hashanah, some after, one cannot separate Ma'aser from beans of one year to exempt beans of the other.

Question: (If one does not know when each plant took root) how may he tithe them?

Answer: He mixes them all together and separates. (A tenth of the mixture contains a tenth of the on Chodosh and a tenth of the Yashan, so) the Yashan in the Ma'aser exempts the Yashan, and the Chodosh in it exempts the Chodosh.

Answer (Rabah): R. Shimon Shezuri holds that Yesh Bilah (things can be mixed uniformly), but Chachamim hold that Ein Bilah.

(R. Yitzchak bar Nachmani citing Shmuel): The Halachah follows R. Shimon Shezuri.

Question (R. Zeira): But Shmuel said that Yesh Bilah only regarding wine and oil!

Answer: R. Zeira did not know that Shmuel taught that we follow the final produce (for Ma'aser, therefore all the beans are Chodosh. R. Shimon Shezuri's solution works even though Ein Bilah.)

Rishonim

Question #1 (Tosfos 13b DH Echad): How can Shmuel say that we follow the final produce? R. Shimon Shezuri follows Hashrashah, and we do not find a Tana that argues!

Answer #1 (Rashi 13b DH Ishtamitsei): We must say that found a Tana that argues. I do not know of such a Tana.

Question #2: Abaye asked that there was no need for Chachamim to follow Hashrashah, because they could rely on Bilah. Rabah answered that Ein Bilah. R. Shimon Shezuri holds that Yesh Bilah; how can he answer the question?

Answer (Ba'al ha'Ma'or): Indeed, R. Shimon Shezuri holds that we follow the final produce, i.e. when it was picked. He asks Chachamim: you follow Hashrashah, and say that if part was Nishrash after Rosh Hashanah and part before, they must be tithed separately. This is wrong; one can mix them and separate from the mixture!

Note: This is Answer #2 to Question #1. Shmuel holds like R. Shimon Shezuri himself really holds.

Rambam (Hilchos Ma'aser Sheni 1:8): Even if rice, poppy or sesame took root before Rosh Hashanah, it is tithed according to when the produce is finished, in the coming year. The same applies to Mitzri beans: if some took root before Rosh Hashanah and some after, mixes them all together and separates Terumah and Ma'aser from everything together, for we follow the final produce.

Question (Ra'avad): If we follow the final produce, there is no need to mix everything together! We hold that Yesh Bilah only for wine and oil!

Kesef Mishneh: The Ra'avad's second question is, even if you will say that Bilah is needed, it does not help!

Answer #1 (and Answer #2 to Questions #1 and #2 - Ri Korkus and Radvaz): Shmuel explains R. Shimon Shezuri. Yesh Bilah Gemurah (perfect mixing) only for wine and oil. R. Shimon says to do Bilah for Mitzri beans only because we follow the final produce. Really, it is all Chodosh; he is stringent to require Bilah, lest the owner does not realize that some was finished before Rosh Hashanah. This concern is only regarding Mitzri beans, and only when some was Nishrash before Rosh Hashanah (Radvaz). Alternatively, we are afraid lest people think that it is like other Yerakos for which we follow when it was picked (Ri Korkus).

Answer #2 (Mar'eh ha'Panim Shevi'is 5b DH Tani and Aruch ha'Shulchan ha'Asid Zera'im 118:26): The Rambam requires Bilah not because of Chodosh and Yashan. Rather, it is in order to tithe from seeds on Yerek and vice-versa. He requires this only for Mitzri beans, for some plant them for the seeds and some only for Yerek (to eat). Here he discusses when it was planted Stam. In Halachah 10 he discusses when it was explicitly planted for the seeds or for eating.

Answer #3 (Ri Korkus and Kesef Mishneh): The Rambam teaches that one may mix them together and tithe, because we follow the final produce. It we followed Hashrashah, one would have to tithe separately what took root before Rosh Hashanah and what took root after, or to separate from other produce (some Vadai Chodosh and some Vadai Yashan) to exempt this.

Question (Likutei Halachos Rosh Hashanah p. 5b Ein Mishpat 3): Why didn't the Rambam bring Shmuel's law that Ein Bilah except for wine and oil?

Answer (Chazon Ish Shevi'is 7:30): The Rambam teaches that one may mix them and tithe (only) because we follow the final produce, i.e. Ein Bilah. It is clear from Hilchos Terumos (13:4) that the Rambam rules that Ein Bilah. The Ra'avad seeks to clarify the Rambam. He wrote his comments to complete the Mishnah Torah, so one who reads it will know all the Halachos.

Question: How can we rule like Shmuel if we do not know a Tana who holds like him?

Answer (Radvaz): Since no Amora argues with Shmuel, we follow him even if we do not know a Tana who holds like him. Perhaps he knew of such a Tana, or he had traditions that Ein Bilah and the Halachah follows R. Shimon Shezuri.

Question: Even if Yesh Bilah, often we will not know which Ma'aser to take (e.g. in year three and six we take Ma'aser Oni from Chodosh and Ma'aser Sheni from Yashan, and vice-versa in year four)!

Answer #1 (Tosfos 13b DH v'Yitzbor): One can redeem the Ma'aser, consume the money in Yerushalayim and give the Ma'aser to Aniyim. Alternatively, he can separate both Ma'aseros.

Rosh (Hilchos Chalah (printed after Menachos) Siman 6): If a Yisrael and a Nochri are partners in a dough, one cannot separate Chalah from it itself, for part of what he separates (the Nochri's share) is exempt It seems that it is permitted, for all agree that Yesh Bilah for wet things. Surely some of what he separates is the Yisrael's, and mid'Oraisa there is no Shi'ur for Chalah.

Rosh (9): If Se'or of Tevel was mixed with a Chulin dough (i.e. Chalah was separated from it), if one has more flour or a Tevel dough, he should separate from it one part in 24 of the Se'or. If not, he separates from the mixture itself one part in 24 of the entire mixture. This is because any amount of Tevel forbids Mino, so it all became Tevel.

Chazon Ish (YD 196:1): In Siman 1 the Rosh writes that he cannot separate one part in 24 just on his own, because some of it is the Nochri's. Then he says that it is permitted, because mid'Oraisa any amount suffices. Since the Kohen receives the proper amount, this is good enough. However, regarding Se'or of Tevel mixed with a Chulin dough, he requires separating one in 24 of the entire dough! Perhaps there it is as if it is totally Tevel because Ta'am k'Ikar. However, when he separates from elsewhere he only separates for the Se'or! It seems that the Rosh is more stringent about separating from it itself when it all belongs to the Yisrael.

Poskim

Shulchan Aruch (YD 324:11): If Se'or of Tevel was mixed with a Chulin dough, if one has more flour or a Tevel dough, he should separate from it the proper amount, i.e. one part in 48 of the Se'or. If not, he separates from the mixture itself one part in 48 of the entire mixture, for it all became Tevel. The same applies if the Se'or is Chulin and the dough is Tevel.

Tur: R. Peretz says that even when the dough is Tevel and the Se'or is exempt, one may separate from the mixture itself. The custom is to separate from another dough on the mixture. This is an excessive stringency.

Shach (324:18): The Terumas ha'Deshen (190) says that even though the Rosh says Yesh Bilah regarding dough, Ein Bilah regarding Se'or (it is dry). When the Se'or is Tevel one may separate from the dough itself because it makes the dough Tevel. This does not apply when a Nochri's Se'or is mixed with a Yisrael's dough. However, the Tur cites R. Peretz who permits even in this case, and does not say that anyone disagrees. It seems that the Tur, and the Shulchan Aruch, hold that the Rosh says Yesh Bilah even regarding Se'or. However, when a small Tevel Se'or is in a large Chulin dough perhaps he will take only from the Se'or. Therefore, the Shulchan Aruch says that the entire mixture became Tevel.

Rema: L'Chatchilah one should not rely on this. One should not put a Chulin Se'or in a Tevel dough. If he did so, l'Chatchilah he may take from that dough to ferment another dough.

Shulchan Aruch (330:3): If a Yisrael and a Nochri are partners in a dough, Chalah must be taken only if the Yisrael's share has a Shi'ur. One may separate Chalah from it itself.

Beis Yosef (DH Motzasi Kasuv): If one bought a dough from a Nochri and mixed it with a smaller dough of his own, mid'Oraisa his is Batel. The mixture is Chayav only mid'Rabanan, so he cannot separate from another dough (that is fully Chayav) on it. Rather, he separates from the mixture itself. It is not enough to separate the proper amount of Chalah, for Ein Bilah except for wine and oil. Rather, he takes Chalah more than the size of the Nochri's dough, so surely some of the Chalah was from the Yisrael's. We learn this from a mixture of Dam Chatas (which must be put on top of the Mizbe'ach) and blood which must be thrown on bottom (Zevachim 80b).

Rebuttal (Darchei Moshe 324:4): The Tur (324) says that one may separate the proper amount from the mixture itself.