Bechoros Chapter 9, Mishnah 8 - the final Mishnah in the chapter. This is a technical Mishnah, dealing entirely with "what if" questions: what is the halachah when the count gets messed up while tithing animals. We will go through the cases in order.
A wide opening - exiting in pairs:
The first case: The opening of the pen was not made narrow enough to restrict the exit to one animal at a time, and the animals exit two by two. The Mishnah says this does not invalidate the process - we count them in pairs. Even though the one counting says "one, two, three, four", his intention is for the first pair, the second pair, and the third pair, and when the tenth pair exits, the two animals in it are the tithe. The Torah specified a series of ten, and it does not necessarily have to be the tenth individual; it can be the tenth pair, the tenth trio, or the tenth quintet. The rule is: as long as the counting is done in equal units, the tenth unit - whether a single animal or a group of animals - is the tithe.
Two that exited and were counted as one:
However, if the first two exited together, and instead of being counted as a pair they were counted as "one", and the one after them exited alone and was called "two" - the entire count is now disrupted. That single animal called "two" is actually the third animal to exit the opening, since the first two exited as one.
From here on: the ninth to exit is called "eight", the tenth to exit - which is the true tithe - is called "nine" and is not declared as the tithe, and the eleventh to exit is called "ten" and is declared as the tithe. The result is that one of them is the true tithe but was not called by its name, and the other was called the tenth even though it is not a tithe at all. Therefore, "teshi'i va'asiri mekulkalin" - the ninth and tenth are ruined.
What is their status? We treat both of them with a certain degree of holiness, based on the verses. Calling an animal by the name "tenth" endows it with a certain holiness even though the animal was supposed to be the ninth, while the animal that was actually the tenth, even though it was called by an incorrect name, does not have enough holiness to be offered as a sacrifice. Therefore, we treat both of them with the stringencies of both levels:
It is forbidden to work with it.
It is forbidden to shear it.
It is forbidden to take its milk.
We wait until it develops a blemish, and then slaughter and eat it; but until then we do not offer it as a sacrifice, since it is not completely sanctified as a tithe.
An important point must be clarified: In the previous Mishnah we learned that there is no obligation to count out loud, and one can count with their fingers, and the tenth to exit is the tithe. However, this law was stated only in a situation where it is absolutely clear to any onlooker that this is the tenth. Once confusion is created, as in the cases of our Mishnah, the matter is no longer clear. We do not have an exact boundary between "clear to all" and doubt, but from our Mishnah it is evident that a count that became confused - where two animals were counted as "one" and the third as "two" - is not considered clear. Therefore, we are stringent in both directions: nothing may be done with either of the two "tenths", and both are problematic.
The ninth and tenth that exited as one:
Another case: The first eight were counted properly - one, two, three, four, five, six, seven, eight - but the ninth and tenth exited together. From a halachic perspective, there is no such reality as exiting at the exact same moment; one certainly preceded the other, and the second one is the tenth, but this is not discernible to the eye. Therefore, the ninth and tenth are ruined: since it is unknown which of them is the tenth, and both are called by the name "tenth" while only one of them actually is, we treat both of them stringently - we do not offer them as sacrifices and we do not even eat them immediately. Rather, we wait until a blemish develops in them, and then they are eaten in the owner's place of residence.
"Kera leteshiei asiri vela'asiri teshiei" - If he called the ninth tenth, and the tenth ninth:
The next case is fundamentally different. The ninth animal came out, and the counter - who had already counted "nine" in his mind - called it "ten" out loud. Realizing his mistake, he tried to correct it and go back, calling the one that came out after it, the tenth, by the name "nine", thereby making the situation worse; and afterward he called the eleventh one that came out "ten". It turns out that the ninth and the eleventh were counted as the tenth, while the true tenth was not counted as the tenth.
The Mishnah says: "Sheloshtan mekudashin" - all three have a certain level of holiness, and below we will distinguish between their types of holiness. This law is based on verses, and there is a surprising point to it: the application of holiness applies only to the ninth, tenth, and eleventh, and no further. If one of the first eight came out and was called "tenth", it means absolutely nothing; but if the ninth came out and was called "tenth", this partial holiness takes effect upon it.
And what is the difference between the three animals?
"Hateshiei ne'echal bemumo" - the ninth animal that was called tenth is treated with the stringencies of a partial tithe, but it is not offered as a sacrifice since it is not truly the tithe, and one waits until it develops a blemish.
"Ha'asiri ma'aser" - even though it was called ninth, anyone watching knows it was the tenth, and the matter is clear to all. As explained in the previous Mishnah, calling the name is not strictly required, and therefore it is the tithe and is offered as the tithe, after the fact.
"Ve'echad asar karev shelamim" - the eleventh is treated with the law of a shelamim offering.
A shelamim is a completely different type of sacrifice. Although it is an offering of lesser holiness (kodashim kalim), instead of one application of blood, two applications are placed on the altar; the breast and the thigh (the right hind leg) are given as a gift to the kohen, unlike a tithe where the owner eats it all; and it is eaten in Jerusalem and in a state of purity. Thus, the eleventh animal, which was mistakenly called tenth, is subject to the laws of a shelamim.
Does the eleventh create a temurah?
The source of this law is in the verses, and the derivation is complex. In short: in the Torah portion discussing the shelamim there are extra words referring to the animal, "If from the herd" (Leviticus 3:1), and since they are not needed there, they must have an application elsewhere. From the tradition we learned that the intent is for the case before us: one who called the eleventh animal coming out of the doorway "tenth", and did not call the tenth by its proper name.
This raises the question: is it an actual shelamim, or perhaps only like a shelamim for another reason? The touchstone is the law of temurah. Temurah involves an attempt to exchange a consecrated animal with another animal: a person consecrated animal A as a shelamim, found animal B to be nicer, and wants to bring it instead. The Torah forbade doing this, but the action takes effect: animal A and animal B are both holy, and both are offered on the altar.
There is another rule: a sacrifice creates a temurah, but a temurah does not create a temurah. That is, animal A consecrates animal B, but if he tries to exchange animal C for animal B, nothing will take effect. The question is therefore: if a person tries to exchange another animal for the eleventh animal, will it become consecrated? If so, then the eleventh is a full-fledged shelamim; if not, it is a sign that its holiness comes from it being a kind of temurah of the tenth animal that got confused in the calling of its name, and a temurah does not create a temurah.
The Mishnah says: "Ve'osah temurah, divrei Rabbi Meir" - according to Rabbi Meir, the eleventh is a full-fledged shelamim, and if he exchanges another animal for it, that one will also become a shelamim. Rabbi Yehudah disagrees: "Vechi yesh temurah osah temurah?" - in his view, the holiness of the eleventh comes as a replacement for the tithe that was not counted properly, and so it is a temurah, and a temurah does not create a temurah.
"Amru mishum Rabbi Meir: ilu hayah temurah, lo hayah karev" - they replied in the name of Rabbi Meir, who was not present: I did not mean a temurah but an actual shelamim, by virtue of that verse. For in all sacrifices, whether an olah or a shelamim, the original and the temurah are both offered; but with the tithe, the Torah made an exception, that one who exchanges another animal for the tithe, the second one is not offered on the altar at all. And if I thought that the eleventh was the temurah of the tithe, I would not offer it on the altar at all. Rather, it is certain that in this situation, where he called the eleventh a tithe and did not call the tenth that preceded it "tenth", the eleventh becomes something completely new: a shelamim in every respect.
And for the halachah: The law of a shelamim offering indeed applies to the eleventh animal, but it does not create a temurah. It is a shelamim, and nothing beyond that.
He called all three of them tenth:
The final case is similar to the previous one, except that here the ninth, tenth, and eleventh were counted - and all were called "tenth." In the previous case, he called the ninth and eleventh tenth, but did not call the tenth tenth; here, he called all three tenth. What is the law?
"Kara lateshi'i asiri" - if he called the ninth tenth. We already learned in the previous line that partial sanctity applies to it: it is not offered, and it is forbidden to be eaten until it develops a blemish. "Vela'asiri asiri" - and to the tenth he called tenth. He called it properly, and therefore it is obvious that its status is ma'aser. "Vela'achad asar asiri - ein achad asar mekudash" - and to the eleventh he called tenth, the eleventh is not sanctified. Calling the eleventh animal tenth accomplishes nothing, and it is just like any animal that one calls tenth where it is meaningless. For the designation of tenth to take effect, it must be counted with nine preceding it. The reason is also derived from the verses: since the tenth was properly counted as the tenth, the count of ten was concluded, and the one that follows it can no longer be called tenth; it is not the eleventh, but rather the first of a new count.
"Zeh haklal":
"Kol shelo ne'ekar shem asiri mimenu - ein achad asar mekudash" - any case where the name tenth was not uprooted from it, the eleventh is not sanctified. The phrasing uses a double negative, and it means: in any situation where the designation of tenth was not uprooted from the tenth animal, meaning it was properly called tenth - the eleventh is not sanctified, even if he called it tenth.
The phrase "Zeh haklal" always comes to include an additional case, and here too: it includes a case where there is no need to say anything at all. The tenth emerged and was not called by any name, but it is clear to any onlooker that this was the tenth, and afterward he called the eleventh "tenth" - since the designation of tenth was not uprooted from the tenth, meaning it was not called by a mistaken name, it is the ma'aser and it is offered, while the eleventh is nothing. Even if he calls it "eleventh" verbally, in practice it is number one: a new count begins from scratch, with no restriction on that animal.
And with this, with God's help, we have concluded Tractate Bechoros. The next in line, God willing, is Tractate Arachin - and with the precise pronunciation: Arachin.