**Kinim, Chapter Three, Mishnah Two**

**Introduction**

Our mishnah is a direct continuation of yesterday’s mishnah. In yesterday’s mishnah we discussed scenarios where the two women brought the same number of pairs of birds. Today’s mishnah deals with cases where one woman has more pairs than the other.

**Mishnah Two **

1) If one [pair] belonged to one woman and two [pairs] to another, or [even] three [pairs] to another, or [ten] pairs to another or a hundred to another, and he offered all of them above, then half are valid and half are invalid.

2) [Similarly], if he offered all of them below, half are valid and half are invalid.

3) [If he offered] half of them above and half below, then the [number of birds as there is in the] larger part are valid.

4) This is the general principle: whenever you can divide the pairs [of birds] so that those belonging to one woman need not have part of them [offered] above and part [offered] below, then half of them are valid and half are invalid;

5) But whenever you cannot divide the pairs [of birds] without some of those belonging to one woman being [offered] above and some below, then [the number as there is in] the larger part are valid.

*Explanation*

**Section one**: If for instance one woman had two pairs and the other woman had three pairs, and they were all mixed up and he offered them all above the red line on the altar, then half are valid as olot, because it is certain that of the ten birds, five were olot.

**Section two**: Similarly, if he offers half of them below, then half are valid as hataot, because it is clear that five of the birds are hataot.

**Section three**: In this case, the number of birds that are valid is equivalent to the number of pairs brought by the woman with the larger number of pairs. Let’s take a case where one woman brought two pairs and another woman brought three pairs. If the priest offered five birds below the line and five birds above the line, three birds are valid. This is because even if of the five birds he offered above, four of them belonged to the woman who brought two pairs, then two are for sure valid and two are for sure invalid because they should have been hataot. The fifth bird which had to have belonged to the other woman, is also valid as an olah. And if of the five birds, all belonged to the woman with three pairs, three are certainly valid as olot. However, two are certainly invalid because they should have been hataot.

The same will work no matter what numbers we plug in. If one woman brought four pairs and the other woman brought six pairs, and the priest offered ten birds above and ten below, then six of the birds offered above are valid as olot. Even if all eight birds from the first woman were offered above, four are valid and then two of the other birds which belonged to the other woman will also be valid. And if all of the birds belonged to the second woman who brought ten pairs, then six are valid. But four have to be invalid because they should have been hataot.

You mathematicians out there should try it out for yourself with other numbersyou’ll see, it always works out.

**Section four**: The mishnah now provides the general rule. If it is possible that he offered all of the birds of one of the women above and all of the birds of the other woman below, then half of the birds are valid. This is the case if the women bring the same numbers of pairs. If each brings, say, five pairs, and he offers five above and five below, it is possible that all of one woman’s birds were offered above and all of the other’s birds were offered below. Half will be valid.

**Section five**: However, if it is not possible that all of the birds that were offered above and below belonged to the same woman, then the number of birds valid is equal to the larger number of pairs. Thus if one woman brought six and one brought four, and he offered ten above, and ten below, it is not possible that all ten above belonged to one woman and all ten below belonged to the other woman. Therefore, six are valid, equivalent to the larger number.