And we learned in a mishna (77b) that in a case where sacrificial portions from unblemished burnt offerings became mixed with sacrificial portions from blemished burnt offerings, which are disqualified, Rabbi Eliezer says: If the head of one of them was sacrificed on the altar before they knew of the blemish, all the heads should be sacrificed, as it is assumed that the head of the disqualified animal was the one already sacrificed on the altar. This indicates that even with regard to slaughtered animals, if they were rejected from the altar due to being in a mixture, they are not permanently rejected, but are fit after the fact.

The Gemara explains that this mishna affords no proof, as Rabbi Eliezer states his ruling in accordance with the opinion of Ḥanan the Egyptian, who maintains that even slaughtered animals are not permanently rejected. As it is taught in a baraita that Ḥanan the Egyptian says, with regard to the two goats of Yom Kippur, the one sacrificed to God and the scapegoat designated to be sent to Azazel: Even if the blood of the sacrificed goat is already in the cup where it was collected and the scapegoat dies, the sacrificed goat is still a fit offering, and the priest brings another goat and joins it to this slaughtered goat to serve as the scapegoat. By contrast, the other tanna’im, who maintain that slaughtered animals are rejected, hold that once they have become rejected due to being in a mixture they are no longer fit for sacrifice, as stated by Rava.

§ Concerning a similar case, Rav Naḥman says that Rava bar Avuh says that Rav says: With regard to a ring used in idol worship, from which it is prohibited to derive benefit and which is not nullified even in a ratio of one in one hundred, that was intermingled with one hundred permitted rings, and subsequently one of them fell into the Great Sea [Yam HaGadol], they are all permitted. The reason is that we say: That ring that fell into the Great Sea is the prohibited ring.

Rava raised an objection to Rav Naḥman from the mishna: With regard to all the offerings that were intermingled with animals from which deriving benefit is prohibited, even if the ratio is one in ten thousand, they all must die. According to the opinion of Rav, that we say the one that was lost is the prohibited item, why must they all die? Let us say, with regard to the first animal that died, that the prohibited animal died, and the rest should be permitted.

Rav Naḥman said to Rava: Rav states his ruling in accordance with the opinion of Rabbi Eliezer, as we learned in the mishna that Rabbi Eliezer says: If the head of one of them is sacrificed on the altar before the priests knew of the blemish, all the heads should be sacrificed, as it is assumed that the head of the disqualified animal was the one already sacrificed on the altar.

Rava asked Rav Naḥman: But doesn’t Rabbi Elazar say: Rabbi Eliezer permitted the sacrifice of all the heads only if they were sacrificed two by two, as at least one of them is certainly permitted; but he did not permit them to be sacrificed one by one, in case the priest sacrifices the prohibited head by itself? How, then, can Rav Naḥman permit the rings without qualification? Rav Naḥman said to Rava: I too am saying that Rav permits the rings only if they are sold two at a time, in which case one of them is certainly not from idol worship.

The Gemara discusses a similar case. Rav says: With regard to a ring used in idol worship that was intermingled with one hundred permitted rings, and then forty of them became separated to one place, and the other sixty became separated to another place, so that they are now two distinct groups of rings, if one ring from the group of forty became separated from them and then became intermingled with other rings, it does not render them prohibited. But if one ring from the other sixty became separated from its group and became mixed with other rings, it renders them prohibited.

The Gemara asks: What is different concerning the case in which one ring from the group of forty separated, that it does not render the other rings prohibited? The reason is that we say: The prohibited ring is in the group that contains the majority of the rings, i.e., it is in the group of sixty. If so, in the case where one ring from the group of sixty became separated and became intermingled with the other rings, we should also say that the prohibited ring is still in the group that contains the majority of the rings, i.e., it is one of the fifty-nine remaining rings. Rather, Rav’s statement was as follows: If all forty became separated to one place, where they became intermingled with other rings, the forty rings do not render those other rings prohibited, as it is assumed that the prohibited ring is in the group of sixty. Conversely, if all of the sixty rings became separated to one place, where they became intermingled with other rings, the sixty rings render those other rings prohibited.

Rav Yehuda, who said this statement citing Rav, added: When I said this ruling in the presence of Shmuel, that if the forty rings became intermingled with others they do not render them prohibited, he said to me: Disregard this halakha with regard to the case of idol worship, as this prohibition is so stringent that its uncertainty and its compound uncertainty are prohibited forever, i.e., no matter how many uncertainties are added they are all prohibited.

The Gemara raises an objection to the opinion of Shmuel from a baraita: An uncertainty of idol worship is prohibited, but its compound uncertainty is permitted. How so? With regard to a cup used in idol worship that fell into a storeroom full of cups, they are all prohibited. If one of these cups separated from the rest and fell into a group of ten thousand other cups, and from that ten thousand cups a single cup fell into ten thousand other cups, they are permitted. This baraita teaches that only one uncertainty is prohibited, not a compound uncertainty.

The Gemara explains: This is a dispute between tanna’im, as it is taught in a baraita (Tosefta, Terumot 5:10) that Rabbi Yehuda says: Prohibited pomegranates from Badan, which are too significant to be nullified, prohibit a mixture in any amount. How so? If one of them fell into a group of ten thousand other pomegranates, and one of that group fell from that ten thousand into another ten thousand, they are all prohibited, despite the fact that this is a compound uncertainty.

The baraita continues: Rabbi Shimon ben Yehuda says in the name of Rabbi Shimon: If a prohibited pomegranate fell into a group of ten thousand pomegranates, they are all prohibited, as he concedes that these pomegranates are not nullified in a majority. But if one pomegranate from the ten thousand fell into a group of three pomegranates, and one of these three pomegranates fell into a different place, it is permitted, as this is a compound uncertainty.

The Gemara inquires: In accordance with the opinion of which of these tanna’im does Shmuel state his opinion that an item used in idol worship remains prohibited no matter how many uncertainties are involved? If you say that he stated his ruling in accordance with the opinion of Rabbi Yehuda, then even with regard to other prohibitions a compound uncertainty should be prohibited, as Rabbi Yehuda stated his ruling with regard to a prohibited pomegranate, not an item of idol worship. And if Shmuel stated his ruling in accordance with the opinion of Rabbi Shimon, then even in the case of idol worship a compound uncertainty should be permitted, as Rabbi Shimon did not differentiate between different types of prohibitions.

And if you would say that there is a difference according to the opinion of Rabbi Shimon between idol worship and other prohibitions, and he prohibits compound uncertainties only in the case of idol worship, then if so, that which is taught in the baraita cited previously: An uncertainty of idol worship is prohibited but its compound uncertainty is permitted, whose opinion does this represent? It is neither the opinion of Rabbi Yehuda nor the opinion of Rabbi Shimon.

The Gemara answers: Actually, that baraita is in accordance with the opinion of Rabbi Shimon, as he permits a compound uncertainty in all cases. And Shmuel holds in accordance with the opinion of Rabbi Yehuda with regard to one matter, that a compound uncertainty is prohibited in the case of idol worship, and disagrees with him with regard to one matter, as Shmuel does not apply this stringency to other prohibitions.

§ The Gemara continues its analysis. The Master, Rabbi Shimon ben Yehuda citing Rabbi Shimon, says above: If one pomegranate from the ten thousand fell into a group of three pomegranates, and one of these three pomegranates fell into a different place, the mixture is permitted.