Kinim, Chapter Three, Mishnah Four
1) If a hatat, an olah, an unassigned pair of birds and an assigned pair [became mixed up], and he offered them all 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, none is valid except the unassigned pair, and that must be divided between them.
Section one: One woman has a hatat, one woman has an olah. In addition, one of these women has an unassigned pair and the other has an assigned pair, and they all get mixed up (just like usall mixed up!). If the priest offers all of the birds above (a total of six birds) half of them are valid. This is because three are certainly olot (the olah bird and one from each pair).
Section two: If he offers all below, three are valid as hataot.
Section three: However, if he offers half above and half below, then only the birds of the unassigned pair are valid, because their status as an olah or a hatat had not yet been determined. The two women will together get credit for one pair, and they can divide that pair among the two of them. They will then need to bring another pair, and offer one as an olah and one as a hatat. Each loses the hatat or olah that they had brought individually.