Taharos, Chapter 1, Mishnah 5. Our mishnah opens a discussion that will continue into the next mishnah as well: what happens when food that carries one level of tumah gets mixed together with food that carries a lighter level of tumah? Does the mixture follow the stricter side or the lighter one? The answer turns out to depend on how much of each there is.
The ladder of tumah
To follow the mishnah we need one principle that has accompanied us throughout Seder Taharos. Tumah is transmitted in descending steps. Whatever a source defiles ends up one rung lower than the source itself. An av hatumah produces a rishon; a rishon produces a sheni; a sheni produces a shelishi. The ladder is fairly consistent, though it has its exceptions, and liquids in particular behave in ways that overturn nearly all of these rules. There is also a limit to how far down the ladder each type of food is able to travel: the level of shelishi belongs to terumah, and revi'i belongs to kodesh. Ordinary chullin simply does not become a shelishi. Keep that last detail in mind, because the mishnah's closing case depends on it.
The rule of the mishnah
The mishnah lays down its rule: "Ha'ochel shenitma be'av hatumah," an item of food defiled by an av hatumah, along with food "veshenitma bevlad hatumah," defiled by a v'lad hatumah, are "mitztarfin zeh im zeh," reckoned together with each other, and the outcome is "letamei kekal shebishneihen," it conveys tumah at whichever of the two statuses is the weaker one. Where the two pieces depend on each other to produce a measure at all, the resulting mixture is graded by its weaker component.
Why should they need to lean on each other? Because of the shiur. A kabeitzah, the volume of an egg, is the smallest quantity of food that is capable of transmitting tumah onward. Food smaller than a kabeitzah can certainly become tamei itself, but it will not pass its tumah along to anything else.
Two half-eggs
"Keitzad?" How does this work in practice? Take a food that mingles thoroughly, a spread of mashed egg for example. There is "kachatzi beitzah ochel rishon," half an egg's volume holding the status of a rishon, and "vekachatzi beitzah ochel sheni," another half egg's volume holding the status of a sheni. "Shiblan zeh vazeh": the two are stirred into each other. The ruling is "sheni." The combined food ranks as a sheni.
The reason is straightforward. Neither half alone amounts to a kabeitzah, so neither can transmit anything by itself. To reach a shiur they must be counted together, and there is only enough material at the level of rishon to fill half an egg. At the level of sheni, however, there is a full kabeitzah, since the portion that is a rishon can certainly be counted as a sheni for this purpose. The mixture therefore emerges as a sheni.
The mishnah then repeats the case one step lower: "kachatzi beitzah ochel sheni," half an egg of food that is a sheni, "vekachatzi beitzah ochel shelishi," and half an egg of food that is a shelishi. "Shiblan zeh vazeh, shelishi." Stirred together they come out as a shelishi, by precisely the reasoning we just applied at the higher rung.
Two full eggs
Now the mishnah shifts the quantities: "kabeitzah ochel rishon," a full egg's volume of food that is a rishon, "vekabeitzah ochel sheni," and a full egg's volume of food that is a sheni. Each side already possesses a complete measure and requires no help from its neighbor. "Shiblan zeh vazeh, rishon." Once mixed, everything is a rishon: the rishon side owned a whole shiur, enough to work upon the other portion and pull it up to its own rung.
"Chelkan, zeh sheni vezeh sheni." Here is the twist. If you now divide that two-kabeitzah mixture back into two portions of one kabeitzah each, each portion is only a sheni. You did not slice along the line separating the original rishon from the original sheni; the food is thoroughly blended, so no single portion contains a full kabeitzah of rishon-level food. Each half therefore drops to the level of sheni.
The two portions and the loaf of terumah
"Nafal zeh le'atzmo," this one fell by itself, "vezeh le'atzmo," and that one fell by itself, "al kikar shel terumah," onto a loaf of terumah, "pasluhu." Picture the two kabeitzah portions landing on the loaf at separate moments: the first lands and is wiped away, and only afterward does the second land. Their effect is that the loaf becomes pasul, the term used for shelishi status. Portion one, being a sheni, turned the loaf into a shelishi; portion two, also a sheni, contributed nothing further, since the loaf had already reached shelishi.
Notice why the mishnah specifically chose a loaf of terumah for this case. A sheni can only bring something down to the level of shelishi, and ordinary chullin does not receive that status at all. Terumah is the food that is sensitive enough to be affected here.
"Naflu sheneihem ke'echad, asahu sheni." And here is the sharp point of the mishnah. If the two portions fell at the same moment, even though they had been separated from each other, they made the loaf a sheni. Each portion on its own counts as a sheni, but the two of them arriving together once again constitute a full kabeitzah at the level of rishon, and a rishon makes whatever it touches a sheni. This also means that had the loaf been plain chullin rather than terumah, it too would have become a sheni, since chullin does accept the status of sheni.
The thread running through the whole mishnah is this: when there is a full shiur of the higher level of tumah, the mixture follows that higher level; when the portions can only reach a shiur by joining together, we go by the lighter of the two.