14 or 15 out of 48?

The gemara on Nida 54A going onto 54B quotes a braisa that says that a woman who has an 16 day cycle (she sees dam for 8 days then goes 8 days without seeing) will be able to have tashmish with her husband for 15 out of 48 days. First I'll explain how the gemara came up with that number:

There are 6 8 day sets. She sees through the first, third and fifth sets and doesn't see during the second, fourth and sixth. The first set encompasses her 7 day nida period and 1 day of ziva. She then needs a day of shomeres yom for the zava ketana. Then she's muteres to her husband for the rest of set 2 (7 days). When she starts seeing dam again on day 17, she's still in her yemei ziva for two days so she's a shomeres yom. The last 6 days of her third set are during her yemei nida so she's a nida plus she needs one day of her fourth set to complete her yemei nida. That leaves 7 days of her fourth set that she is tehora. Then her fifth set starts during her yemei ziva but this time 4 days are during her yemei ziva so she's a zava gedola which means that she needs 7 clean days before she can become tehora and that leaves only the last day of her sixth set when she is tehora.

The gemara then asks that it should be 14 and not 15. Rashi understands this question one way and all the other Rishonim disagree. First let's understand Rashi's pshat:
The question is only based on the last set. We said that she can start counting her 7 clean days right when the bleeding stops so she'll be tehora on day 48. The problem is that she's in the middle of her yemei nida at that point. She started cycle 5 on the eighth day of her yemei ziva which means that the last four days of bleeding are when she should have been in her yemei nida. That leaves three more days during her sixth set that she's still in her yemei nida so she can't even begin to count which means that she won't be tehora on day 48. So there are only 14 days when she's tehora. The gemara then answers that if you don't see dam during the yemei nida that you could count it as clean days.

This Rashi is extremely difficult to understand. The Rishonim jump all over Rashi because his explanation really goes against everything we have learned. We know that there is always a 7-11 cycle. The first 7 days are yemei nida and the next 11 are yemei ziva (I'm not getting into the Rambam's pshat at all here although this gemara is really a key to understanding his explanation of the cycle.) That's for a normal woman. However, we also know that if a woman sees dam on days 9,10,11 of her yemei ziva (days 16,17,18 overall) that she's a zava gedola. She then must count 7 clean days before she is tehora. Until she counts her 7 clean days she can never become a nida. So in this case, if she saw dam again on day 22, she is not a nida because she still hasn't had 7 clean days since she first saw dam. Even though this is after the 11 so she should be in yemei nida she can't actually become a nida yet. Those are facts that even Rashi agrees to. However, he says that while that's true, the makshan in our gemara held that those days still count as yemei nida inasmuch as she can't start counting her clean days during that time. That's still hard for me to understand.

Tosafos seems willing to accept that but has two serious problems with Rashi:
1. Why are we only bringing up this problem on the 16 day cycle. We should have asked this on the 14 day cycle. The braisa said that she's tehora for a quarter of her days. According to Rashi though that's not true. Her third set of 7 days include 4 of yemei ziva and 3 of yemei nida. So she can't start counting her 7 clean days at the beginning of her fourth set. She must first wait until she's out of her yemei nida. That won't happen until day 5 of the fourth set so that means that she won't be starting anew on day 29. So while it's true that she'll be tehora for 7 out of the first 28 days, it doesn't go on forever. After that she's going to be temeia for a very long time.
2. It sounds from the gemara like it would have been ok had the braisa said 14 out of every 48 instead of 15 but that's not true. It wouldn't be able to start over on day 49 because she first has to finish counting her 7 clean days which could only start after her yemei nida were over. It comes out that she won't be tehora again until day 63.

Apparently Rashi isn't bothered by these questions because he doesn't learn the braisa to mean that she'll be tehora for 14 or 15 out of every 48. Just 14 or 15 out of the first 48. Same thing with the previous case. She's tehora for one quarter of the first 28 days but not a quarter of her days forever. That doesn't seem like pashut pshat in the braisa.

The Aruch Laner answers the first question of Tosafos. He says that Rashi only holds that it's called yemei nida even though she's still in her yemei ziva if she's already passed 30 days since her last cycle started.

Tosafos argues with Rashi and says that the gemara's question is from back on the fourth set. The problem is that she's a zava ketana because the first two days of her third set were during her yemei ziva. Then we say that she keeps just the first day of her fourth set as the shomeres yom and she is tehora on day two of the fourth set. That first day is also the seventh day of her yemei nida so the gemara is asking how could that count as a clean day for yemei ziva. The gemara answers that a clean day during yemei nida could count as the shomeres yom for a zava ketana.

To me, this pshat fits in perfectly in the gemara and makes a lot of sense.