Gemara

(Mishnah - R. Eliezer): If a (Zav or) Zavah checked herself on the first and seventh days that she must count, and found herself to be clean, and did not check on the other days, we rely on Chazakah that also the intermediate days were clean;

R. Yehoshua says, only days one and seven count. Five more clean days are required;

R. Akiva says, only day seven counts.

(Beraisa - R. Eliezer (to R. Yehoshua)): If you are concerned for Tum'ah in the middle, day one should not count! "V'Achar Tithar" obligates immersing after all the (seven clean) days (consecutively, without Tum'ah in the middle).

If we say that unchecked days neither count nor are Soser, due to the Safek (perhaps she saw), people will say that she Vadai saw, and even so it is not Soser!

(Beraisa - R. Shimon and R. Yosi): R. Eliezer's opinion is more reasonable than R. Yehoshua's;

R. Akiva's opinion is the most reasonable. However, the Halachah follows R. Eliezer.

Question: If a Zavah checked herself only on days one and eight, and found herself to be Tehorah, what is the law according to R. Eliezer?

Does he require checking at the beginning and end? Or, perhaps it suffices to check at the beginning alone?

Answer #1 (Rav): Here also, R. Eliezer is Metaher.

Answer #2 (R. Chanina): He requires the beginning and end. The end is missing.

(Rav): If a Nidah (really, a Zavah) was Mafrish on the third day, she counts it towards seven clean days.

Question (Rav Sheshes): (The Kusim say this!) Does Rav hold like the Kusim?!

Answer (R. Yirmeyah bar Aba): He means that she may count the days after the third day.

Even if she did not check again until the seventh (clean) day, the end alone suffices. One might have thought that only the beginning suffices, for then she is Muchzekes Tehorah.

Question (R. Yosi b'Rebbi Chanina): A Beraisa (29b) discusses a To'eh (one who does not know when she gave birth. The Tana holds that it is a Mitzvah to immerse at the first opportunity.) If the beginning is not essential, every day in the first week she should (check and) immerse during the day. Perhaps she was Yoledes b'Zov, and today she finished seven clean days!

Rather, because she did not check the first day, she may not immerse.

Answer (Ravin): The Beraisa is like R. Akiva, who requires counting the (seven clean) days "in front of us" (according to Beis Din, i.e. checking each day. Chachamim disagree.)

Question: What is the source that Chachamim disagree?

Answer (Beraisa): If a woman says "I saw blood one day" (she does not know when), she immerses seven times (the next seven nights) due to Nidah, and two times during the day due to Zavah;

If she says "I did not see," she immerses 15 times.

Objection (Rava): It is absurd to immerse more often when she did not see!

Correction: Rather, if she does not know how she saw, nor whether it was during the days of Nidah or of Zivah," she immerses 15 times:

This shows that Chachamim require checking each day.

1. Rejection (Rav Acha brei d'Rav Yosef): We corrected the Beraisa. If we amend it differently, the proof goes away! I.e. she says "I do not know whether or not I counted, or how many days I counted..."

Rishonim

Rambam (Hilchos Isurei Bi'ah 6:22): If a Zavah checked and found herself Tehorah on the first day, and also on day eight, she has Chezkas Taharah. If she checked on day three of Zivah and found that the blood stopped, and did not check on the first of the seven clean days, and on the seventh day she found that she is Tehorah, she has Chezkas Taharah.

Rosh (10:5): The Ra'avad rules like Rav, because Rav Sheshes and R. Yirmeyah discussed Rav's opinion. This shows that they hold like him. Also, we challenged Rav from the Beraisa of To'ah, answered that the Beraisa is like R. Akiva, and proved that Chachamim disagree. This shows that the Halachah follows Rav. Rav Acha rejected the proof, but it is a mere Dichuy. Therefore, nowadays that every woman is a Safek Zavah, she must be Mafsik b'Taharah to check herself, to know that the blood stopped. She must check herself each of the seven days. B'Di'eved, if she checked only the first and seventh day, this is called seven clean days. We hold like Rav, who says that the beginning or end suffices. If she did not check until day eight, this is not called counted. She must check within seven days. The Ra'avad did not hear about one who checked in the middle, but not at the beginning or end. Presumably, we are lenient, for if a Nidah checked herself on the morning of the seventh day, but was not Mafsik Bein ha'Shemashos, and days later she found herself Temei'ah, she has Chezkas Taharah. In both cases, she must check. In both cases, the Bedikah in the middle suffices. The Ba'al ha'Ma'or says that we cannot learn Bedikah of a Zavah, who requires seven clean days, from a Nidah, who requires merely Hefsek Taharah Bein ha'Shemashos. I see no Safek. Presumably, the middle is better than the end, for she was Muchzekes Tehorah for all the days after the Bedikah.

Poskim

Shulchan Aruch (YD 196:4): L'Chatchilah, she must check twice on each of the seven days, once in the morning and once close to Bein ha'Shemashos. If she checked only once in the seven days, whether it was on the first or last day or in the middle, since she checked on the day before the seventh and found herself Tehorah, it counted for her.

Shach (8): The one time is amidst the seven days, in addition to the Hefsek Taharah beforehand.

Shulchan Aruch (ibid.): If she did not check in all seven days, and on day eight she checked and found herself Tehorah, only day eight counts, and she completes (six more days). Some say that she must check on days one and seven, and one should not be lenient. She must check by daylight, and not through a lamp. B'Di'eved, even through a lamp helps

Noda bi'Yehudah (2 YD 128): The Ra'avad rules like Rav. Since day one or seven suffices, i.e. we do not need specifically days one and seven, reasoning teaches that any day in the middle suffices. However, R. Chanina requires specifically days one and seven. The Ra'avad's proof from Nidah does not apply to R. Chanina, since she needs to check only one day, and the Rosh's question does not apply.

Hagahas Sachar Tov: See Dagul me'Revavah (brought below. There, the Noda bi'Yehudah wrote that a day in the middle helps even according to Semag, who rules like R. Chanina.). This requires investigation.

Noda bi'Yehudah: The Ba'al ha'Ma'or, in his comments on the Ra'avad's Ba'alei ha'Nefesh (Sha'ar ha'Sefirah, Saif 3) asked 'also, why does he rely on checking in the middle? This is like Rav, and R. Chanina argues!' Why didn't the Ba'al ha'Ma'or ask earlier (Sa'if 2) why the Ra'avad rules like Rav?! He waited until here in order to argue with both rulings of the Ra'avad like Rav.

Noda bi'Yehudah: I have a Chidush from reasoning. If she checked days one and three, this is not enough to immerse on day seven. If she checked also day 10, only day 10 counts (for her first checked day). If she checked days one, three, and eight or nine, she may immerse at night. This is obvious if she checked on day nine, for we can ignore day one, and days three and nine count like days one and seven. Even if she checked on day eight, it is the last day, and it joins with day one. Even though more than five days separate them, the Bedikah on day three joins them. I learn from R. Yehoshua. He said 'only the first and seventh days count. Five more clean days are required.' He counts day one (towards the seven). R. Yehoshua agrees that if she checked days one and eight, only day eight counts. Day one cannot join with day eight. Even so, day one can join with day seven and five more days afterwards. The same applies in my case, when she checked one, three and eight. One could reject this. R. Yehoshua's law is a stringency, to be concerned lest she saw in between. Just like he is not concerned for the gap in the middle, he is not concerned for joining with days afterwards. If she did not check on day seven, according to R. Chanina, letter of the law it and future days do not join with day one at all.

Dagul me'Revavah: Semag says 'since the Halachah was not decided, it is proper to be stringent like R. Chanina not to allow more than five days between Bedikos.' If so, even if she did not check day one, but she checked a day in the middle and also day seven, Semag admits that this suffices, as long as she was Mafsik b'Taharah. (This is because there were not more than five days between Bedikos - PF.)

Pischei Teshuvah (6): In Noda bi'Yehudah (ibid.) he said that if she checked days one, three and eight, day eight joins with day one. Even though more than five days separate them, the Bedikah on day three joins them. This is unlike he wrote in Dagul me'Revavah.

Note: I explain the contradiction as follows. Since he allows joining as long as there are no more than five unchecked days in between, why did he need to mention the Bedikah on day one? If even Semag does not require day one, the Hefsek Taharah suffices together with days three and eight!

Pischei Teshuvah (7): The Chasam Sofer (178) is lenient if she already was with her husband, if she surely checked day one or seven. If she checked only a day in the middle, even b'Di'eved we are stringent.