Taharos, Chapter 1, Mishnah 7. Our mishnah moves to a case that anyone who has ever handled dough will recognize immediately. Dough clings. Place two lumps beside each other and they stick, yet they have not become one mass: pull them apart and each one is again its own lump, with its own identity. That in-between state raises a real question in the laws of tumah and taharah. When one of the lumps contracts tumah, what happens to its neighbors that are stuck to it? And what happens once they are pried apart again?
The text begins with two parallel images. First, "Mikratzos noshchos zo bazo", lumps of dough that bite into one another, and then, in the same breath, "vechikarim noshchim zeh bazeh", whole loaves that do the very same thing. The picture is of distinct pieces pressed up against their neighbors until they adhere at the point where they meet.
Tumah from a sheretz
The first case: "Nitmeis achas mehen b'sheretz". One of the lumps in the cluster came into contact with a sheretz and thereby became tamei. The ruling is "kulan techilah": the entire group takes on the status of a rishon.
To follow this, keep the ladder of tumah in mind. A sheretz is an av hatumah, what we might call level zero, the source itself. Whatever the sheretz touches becomes a rishon. That rishon can pass tumah on and make something a sheni. A sheni can go one step further and render terumah a shlishi, and in the case of kodesh the chain continues one more rung to a revi'i.
Now, one might have imagined that our clinging lumps of dough would work like a row of falling dominoes: the lump the sheretz touched becomes a rishon, the lump stuck to it becomes a sheni, the next one a shlishi, and so on down the line. The mishnah tells us otherwise. Because they are attached, they are treated as a single unit receiving tumah from the sheretz, so every one of them is a rishon.
"Parshu, kulan techilah" - and if they were then separated from one another, each one remains a rishon. The status they acquired while joined stays with them even after they no longer touch.
Tumah from liquids
"B'mashkin, kulan sheniyos": where the tumah reached the dough by way of one of the seven liquids, the outcome for the whole cluster is sheni. The Chachamim ruled that tamei liquids operate on the level of a rishon, and consequently whatever they touch drops to sheni. Here as well, the adhering mass absorbs the tumah as a single body, so no individual lump ends up on a lower rung than the rest. "Parshu, kulan sheniyos": even after the pieces are pulled apart, each one holds on to its status as a sheni.
Tumah from hands
"B'yadayim, kulan shlishiyos" - if the source was a person's hands, all of them are a shlishi. Hands were given the status of a sheni by rabbinic decree, and that decree stands behind the whole institution of washing our hands before various ritual matters. Since a sheni renders terumah a shlishi, this clause is speaking of dough that is terumah, and the entire cluster becomes shlishi together. "Parshu, kulan shlishiyos" - when they are pulled apart, each lump remains a shlishi.
The principle running through the whole mishnah is one and the same: dough that is stuck together receives tumah as one body, all of it landing on the same rung of the ladder, and each piece then carries that rung with it when it goes its separate way.