When the number of pairs brought by each
woman is not equal, for example this woman has one pair, another
has two pair, another has three pair, another has ten pair, and
another has one hundred pair, if he brought the birds of two of
these women at the upper part of the Mizbayach as Olos half are
kosher and half are possul. If he brought all the birds of two
women at the lower part of the Mizbayach as Chato'os half are
kosher and half are possul. If he brought half at the upper part
and half at the lower part, the same number of birds as are in
the larger of the two women's groups is kosher. (Some of those
birds that are kosher will have originated in the larger group
and some in the smaller group.)
This is the rule, any situation in which the two women's groups
are the same size, so it is possible to divide the kinim evenly,
and no one woman's birds will be forced to be partly at the upper
part of the Mizbayach and partly at the lower part, half of the
birds are kosher and half are possul. Any situation in which the
women's groups are of unequal size so the kinim cannot be divided
evenly, and one woman must have brought some birds at the upper
part and some at the lower part, the same number of birds as are
in the larger group is kosher.
The Mishna mentions groups of 1, 2, 3, 10, and 100
kinim, each belonging to a different woman. the Rav explains
that the Mishna is referring to various cases of two women. Each
of the women has 1, 2, 3, 10, or 100 kinim (but both do not have
the same number). The two women's groups become mingled.
According to the Tiferes Yisroel, the case of the Mishna is of
five women who have 1, 2, 3, 10, and 100 kinim respectively. All
116 kinim become mingled in a single group.
The cases presented below follow the explanation of the Rav.
Example of One Case of the Mishna
Two women have different numbers of kinim stumos that become
mingled with each other. For example, Rochel has three kinim and
Leah has five kinim. The Kohain mistakenly brought all 16 birds
as Chato'os (or all as Olos).
If all the birds were brought as Chato'os each woman
fulfilled her obligation to bring her Chato'os. That is, half of
each woman's birds were brought properly. None of the Olos was
Rochel brings three additional birds as Olos, and Leah
brings five additional birds as Olos. (If the original birds
were all brought as Olos, then the additional birds are
Example of Another Case of the Mishna
Rochel had three kinim and Leah had five, as in the previous
case. The Kohain mistakenly brought half of the sixteen birds as
eight Chato'os and half as eight Olos.
Result in the Worst Two Cases
If the Kohain brought all six of Rochel's birds as Chato'os, then
the other two Chato'os that he brought were Leah's. The eight
Olos were Leah's remaining eight birds. Thus Rochel's obligation
to bring three Chato'os is satisfied, but she has not brought any
Olos. Leah has brought two Chato'os and eight Olos. (Three of
Leah's eight Olos should have been brought as Chato'os.)
Rochel's obligation to bring three Olos has not been fulfilled.
Leah has yet to bring three of the Chato'os of her obligation.
In an analogous outcome, all of Rochel's six birds were brought
as Olos, and the other two Olos were Leah's. The eight Chato'os
were Leah's remaining eight birds.
In both these worst cases, five valid Chato'os and five valid
Olos were brought. Obligations to bring three Chato'os and three
Olos remain unfulfilled.
In the language of the Mishna, hamerubeh kosher, the same
number of birds as are in the larger group is kosher. In this
example, the larger group was Leah's ten birds, and that number
of birds, five Chato'os and five Olos, is kosher. The remaining
six birds might be possul. However, although the number of birds
that are kosher equals the size of Leah's group, the specific
birds that are kosher are not necessarily all Leah's. The
comment, below, discusses how to replace the korbonos that are
Eight of the sixteen birds were brought as Olos. (In
the worst case all eight were Leah's.) This forces at least two
of Leah's ten birds to be Chato'os, which means they are kosher.
The total deficit of the two women of three Chato'os
and three Olos is the worst case maximum. Depending on whose
birds the Kohain actually brought as Chato'os and Olos the two
women might have lost fewer than three of each korbon -- possibly
not any. Thus, the obligations are all sfaykos.
Therefore, the two women each individually, or both jointly, buy
three more birds for Olos. If the Olos are brought jointly the
agreement is that they will belong to the women according to each
woman's remaining obligation. The women each individually or
both jointly buy only one replacement Chatos, because of the
limitation on Chato'os bought for a sofaik, as discussed in the
previous Mishna and the appendix.
Alternative Approach to the Reason
In the best case, the Kohain
would bring five of Leah's birds as Chato'os and five as Olos.
Then none of the sixteen birds is brought improperly.
But if the Kohain brings six of Leah's ten birds (and two of
Rochel's) as Olos , one is possul. If he brings seven as Olos,
two are possul. If all eight birds he brought as Olos were
Leah's, three are possul. There is no outcome in which four or
more of Leah's birds can be possul because the Kohain brought
only eight Olos altogether.
If eight of Leah's birds were brought as Olos, two were Chato'os,
and both were kosher. All six of Rochel's birds would have to
have been brought as Chato'os, and three of them are kosher.