Kinim, Chapter Three, Mishnah One
The first mishnah of chapter three relates to the halakhot found in mishnayot 1:2-3 regarding pairs of sacrificial birds that become mixed up.
1) When are these words said? When the priest asks advice.
2) But in the case of a priest who does not seek advice, and one [pair] belongs to one [woman] and one to another, or two [pairs] to one and two to another, or three [pairs] to one and three to another, and he offered all of them above [the red line], then half are valid and half are invalid.
a) [Similarly], if [he offered] all of them below, half are valid and half are invalid.
b) If [he offered] half of them above and half of them below, then of those [offered] above, half are valid and half are invalid, and also of those [offered] below, half are valid and half are invalid.
Section one: If birds get mixed up and the priest comes to ask advice as to what to do with them, he is taught the halakhot we learned in 1:2-3.
Section two: The mishnah how goes on to explain what happens if he does not seek advice and just offers all of the mixed up sacrifices. In today’s mishnah the scenario is simple for the numbers of pairs belonging to each woman is equal. Tomorrow’s mishnah will introduce much more complicated scenarios. If the number of pairs are even, then half will be valid and half will not be valid.
Thus if he sprinkles all of the blood above the red line on the altar, as is done with the olah, then all of the olot are valid, and all of the hataot are invalid.
If he offers all of the blood below the red line, as is done with the hatat, then all of the hataot are valid, and all of the olot are invalid.
If he offers half above the line and half below the line, then half of each group are valid. It turns out that in all of these cases, each woman gets credit for half of the birds that she brought.
As an aside, I think it is interesting that the mishnah deals with a case where the priest did not ask advice from sages before sacrificing the mixed-up birds. I think that we might read into this a bit and see that priests probably did not follow rabbinic halakhot as closely as the rabbis might have liked, and therefore the rabbis have to figure out how to proceed in such a situation.