APPLYING R. YOCHANAN'S ANSWER TO OTHER CONTRADICTIONS IN THE POSITIONS OF BEIS HILLEL AND BEIS SHAMAI
Question: A contradiction could be raised from their positions regarding the permissibility of using the Ali as a meat cutting board.
Beis Shamai prohibits (Kli Sh'Melachto l'Isur)
Beis Hillel permits (Tzorech Gufo).
This demonstrates the Chumra of Beis Shamai regarding Simchas Yom Tov, in contradistinction to our Mishnah.
Answer (R. Yochanan): Reverse their positions regarding the Ali.
Question: But there are alternative explanations!?
Beis Shamai could be relying on Deker Na'utz for their Kula in our Mishnah.
Beis Hillel might view the Ali as a K'li.
Question: A contradiction might be raised from their positions regarding spreading out (m'Abed) or raising (Muktzah) the hides.
Answer (R. Yochanan): Reverse their positions regarding stepping on the hides.
Question: But there are other explanations!?
Beis Shamai could be relying on Deker Na'utz.
Beis Hillel might be lenient here because the hide has a Yom Tov purpose.
Question: A contradiction might be raised from their positions regarding removing the doors of the stores (where Beis Shamai prohibits their removal and Beis Hillel even permits their being replaced).
Answer (R. Yochanan): Reverse their positions.
Question: But there are other explanations (Beis Hillel may not recognize Binyan and Stirah by Kelim)!?
MISHNAH: DESIGNATING BIRDS FOR USE ON YOM TOV
(Beis Shamai): One must have handled the birds before Yom Tov in order to designate them for use on Yom Tov.
(Beis Hillel): It is sufficient to stand and state which birds are going to be taken.
DEFINING THE MACHLOKES
(R. Chanan b. Ami): The Machlokes only applies to the first offspring.
These are normally left in the coop.
Beis Shamai requires additional signs of designation to avoid Tiltul Muktzah).
Not so by subsequent sets of offspring, where they would agree that stating which birds will be taken would suffice.
Question: Why does Beis Hillel require specific designation at all (let his selection on Yom Tov indicate retroactively his intent Erev Yom Tov)!?
Answer: Beis Hillel does not hold of Bereirah.
Question: But we find him holding Bereirah in the Mishnah regarding Tumas Pesachim (where the designation could be made even after the person died)!?
Answer: That Mishnah was explained by Rabah (and by R. Oshiya) as referring only to the future status of the openings from that point onward, not retroactively.
Answer (Rava): Beis Hillel meant retroactive Tum'ah and Taharah, but a general designation by the birds is not sufficient to prevent him from changing his mind after handling a bird (resulting in Tiltul Muktzah).
Question: Then how is stating his intent (without handling the specific birds) sufficient!?
Answer: He may make his verbal designation when he recognizes the birds before Yom Tov.
If, however, he is attempting to rely on his selection on Yom Tov, we would not permit it given our concern that he will handle Muktzah while making his selection.
Alternately, we are concerned that he will be disappointed with all of the available birds and (if he is not bound by his previous designation) he will go without Simchah on Yom Tov altogether.
MISHNAH: WHEN MIGHT THE BIRDS BE OTHER THAN THE DESIGNATED ONES
If the designated birds are black and the ones he finds are white (or the reverse), or if he designated two and finds three, they are all prohibited from use.
If he designated three and finds two, they are permitted.
If they were originally within the nest and are now on the shelf in front of the coop, they are prohibited.
If, however, no other birds were around the coop before Yom Tov, then these birds are permitted.
ASSUMPTIONS OF THE FIRST CASE OF THE MISHNAH (ROV VS. KAROV)
Question: That case seems obvious (they are surely not the same birds if they are a different color)!?
Answer: We might have permitted the birds when he designated black birds in one nest and white birds in the other, under the assumption that they traded places (rather we give precedence to Rov over Karov).
Question: Is this Mishnah a support for R. Chanina who gives precedence to Rov over Karov!?
Answer: It need not be, as the Mishnah may be explained (as Abaye does) where the nest has a shelf in front of it, making all (non-designated) birds just as Karov (and surely the Rov).
DESIGNATING TWO AND FINDING THREE
The Isur is based on the following Ma Nafshach:
If these birds are all new, they are Asurim.
If one of them is new, then it is not Batel since it is a Davar she'Yesh Lo Matirin.
DESIGNATING THREE AND FINDING TWO
Question: On what basis are these permitted?
Answer: We assume that two remained and one flew away.
Question: Does this Mishnah side with Rebbi (in his argument with Rabanan, and thus against the Halachah)?
(Rebbi): One who finds 200 in a box where he placed 100 of Ma'aser must view them as a mixture of Chulin and Ma'aser.
(Rabanan): The entire 200 is Chulin (since Ma'aser funds are normally kept segregated).
(Rebbi): If he found 100 after leaving 200 he presumes them to be half of his Ma'aser funds.
(Rabanan): They are all Chulin.
In our case, the Rabanan would, apparently, view the two remaining birds as not the same as the originally designated trio!?
Answer: The Rabanan could concur with our Mishnah given the teaching of R. Yochanan and R. Elazar that money is less likely to be out of its place than birds.
Question: Why did we need to force this distinction between money and birds, if in the scenario of "two money-sacks" there is no dispute between Rebbi and Rabanan?
There is a Machlokes between R. Yochanan and R. Elazar as to the case in which Rebbi and Rabanan argue.
(One view): They only argue when the 200 were in two sacks of 100 each, but they would agree that it is all Chulin if they were in one sack.
(The other view): They argue only when the 200 was in one sack, but if it were split then all agree that this is half of the original Ma'aser.
The distinction between birds (which hop) and money (which does not) is needed only according to the first view (to explain why Rabanan view both sacks as having been taken, but view only one bird as having left).
But according to the second view, the distinction is clear!?
Answer (R. Ashi): When speaking of the 200 in one sack, they meant two sacks which were tied together, and the parallel case in our Mishnah is where the birds were tied together, as well.
Birds, given their motion, untie from one another.
Coin sacks, on the other hand, do not.
(Rebbi): The tie between coin sacks also is prone to come undone (and one might inadvertently take one sack and leave the other).