Niddah, Chapter 9, Mishnah 6. This chapter deals repeatedly with blood that is discovered somewhere and the problem of assigning it to a source. Our mishnah returns to the case of women who shared a single bed, but now it pays close attention to where in the bed each woman was lying, since a sleeping person shifts about only so far.
The mishnah begins: "Shalosh nashim", three women, "shehayu yesheinos bemitah achas", who spent the night in a single bed. "Venimtza dam", blood was afterward discovered, "tachas ha'emtza'is", at the spot occupied by the one in the middle. The verdict is "kulan temeios", not one of them is cleared. Whoever lay in the center could have been reached by a neighbor rolling toward her from either direction, so all three remain under suspicion.
Blood found at the inner or outer edge
"Tachas hapnimis", suppose instead that the blood shows up at the place of the innermost woman, the one whose spot was up against the wall. The ruling is "shtayim hapnimiyos temeios vehachitzonah tehorah", the two who lay further in are both temeios, while the third, whose place was at the open side of the bed, is tehorah.
Two assumptions are at work here at once. On the one hand, we do assume that women shift position during the night, which is why the blood is not attributed to the woman above whose place it was found alone. On the other hand, we assume that such movement has limits: a sleeper rolls to the next place over, not clear across the bed. The woman lying at the outer edge is thus too far removed from the wall to be a realistic candidate, and she remains tehorah.
Flip the case around and the identical logic produces the mirror result. "Tachas hachitzonah", the blood is found at the place of the woman on the open side, the one positioned furthest away from the wall. Here the mishnah rules "shtayim hachitzonos temeios vehapnimis tehorah": the pair nearer the outside are both temeios, and the woman whose spot was alongside the wall stays tehorah.
Rebbi Yehudah: how did they get into the bed?
"Amar Rebbi Yehudah, eimatai", Rebbi Yehudah asks when this ruling holds, and answers: "bizman she'avru derech margelos hamitah", when the women climbed in and out by way of the foot of the bed. In that case nobody had reason to pass over the outer edge, and the distinctions drawn above stand.
"Aval im avru sheloshtan", but if all three of them got in and out "derech aliyah", by climbing over the long side of the bed, then blood at the outer spot leaves nobody exempt: "kulan temeios". Each of the three, the woman who slept beside the wall included, had to pass across that outer stretch on her way to her place, and any of them may have left the blood behind there.
Examinations, and how many are cleared
In all of these situations, an internal examination can change the picture. "Badkah achas meihen venimtzes tehorah", one of the women examined herself and found herself tehorah, with no uterine blood present: "hee tehorah ushtayim temeios", she is tehorah and the other two are treated as temeios.
Next case: "Badku shtayim", two of the three examined themselves, "umatz'u tehoros", and both came up clean. Then "hen tehoros vehashlishis temeiah", that pair is tehoros, and the whole doubt now rests upon the woman who did not check.
"Sheloshtan umatz'u tehoros", but if all three examined themselves and all three were found tehoros, the ruling is "kulan temeios", all of them are temeios. This is not a contradiction. Blood was undeniably found in that bed, so one of the three is certainly its source; the examinations simply failed to reveal which. Having no way to identify her, we cannot single anyone out, so out of doubt we treat every one of them as temeiah.
The parable of the three mounds
To drive the point home, the mishnah brings a comparison from an entirely separate branch of the laws of tumah: "lemah hadavar domeh?", to what is this similar? "Legal tamei", to a mound that carries tumah, "shenis'arev bein shenei", which got confused among two others, "galim tehorim", heaps that are tehorim.
Picture three heaps of stones. One of them contains a corpse buried within it and is therefore tamei; the other two contain nothing and are tehorim. We know for a fact that one of the three carries tumah, but we no longer know which one it is.
"Ubadku echad meihen", one of the heaps was excavated, "umatz'u tahor", and nothing was found inside it: "hu tahor ushnayim temeim", that heap is tahor, while the two that remain carry the status of tumah. Next, "shenayim umatz'u tehorim", two heaps were dug through and neither held anything: "hem tehorim vehashlishi tamei", those two are tahor and the tumah is now pinned on the one heap left. Finally, "sheloshtan umatz'u tehorim", all three were excavated and no corpse surfaced anywhere at all, and the ruling is "kulam temeim": each of the heaps is handled as tamei.
Rebbi Meir and the Chachamim
That last ruling represents "divrei Rebbi Meir", and the mishnah spells out the reasoning standing behind it. Rebbi Meir taught: "kol davar shehu bechezkas tumah", whatever has been established as bearing tumah, "le'olam hu betum'aso", remains permanently in that condition, "ad sheyivada lecha", until it becomes genuinely known to you "tumah heichan hee", in which place the tumah is to be found.
We began with the knowledge that one mound held tumah. If a search establishes with certainty that the tumah lies in one of the other mounds, then this mound may be considered tahor, because the tumah has been located elsewhere. But if all three were searched and the tumah was never found at all, we still have no idea where it went, and the original status is never displaced. Each mound therefore retains its presumption of tumah.
"Vachachamim omrim", the Chachamim take a different view: "bodeik ad shemagia", one keeps digging through a heap until he reaches "lesela o le'avsulah", the bedrock beneath it, or else untouched earth that no spade has ever turned over. A search carried to that depth which uncovers no corpse settles the question, and the heap may then be handled as tahor.
So the Mishnah moves from the practical question of women sharing a bed to a broad principle about unresolved doubt: a known tumah does not simply evaporate because we have looked for it and come up empty, and how much searching it takes before we may declare the matter closed is itself a subject of debate.