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1)

(a) If one wants to transform a cabin with a roof comprising four-Tefachim planks into a Sukah, according to Rebbi Yehudah, Beis Shamai require two acts to rectify it - in addition to shaking the planks, one also needs to remove every second one.

(b) Beis Hillel permit either of the two. According to Rav, Rebbi Yehudah requires shaking the planks or removing every second plank - because of 'Ta'aseh ve'Lo min he'Asuy'.

(c) Rebbi Meir holds that both Beis Shamai and Beis Hillel require the removal of every second plank - because of 'Gezeiras Tikrah'.

(d) Shmuel forbids planks of four Tefachim according to everyone. He might learn like Rav (who only forbids planks of four Tefachim if they total four Amos - even in the middle of the Sukah, as will be explained later). Alternatively, he might establish Beis Hillel's concession of removing only *one* out of two planks - by a Sukah of eight Amos by eight Amos, when a plank is placed on either side of the Sukah first (and then a space, a plank and a space, and so on - resulting in a space of eight Tefachim in the middle, to be filled in with S'chach). This comprises a Sukah with 'bent walls' of less than four Amos (like we explained on the previous Amud), which is Kasher.

(a) According to Rebbi Yehudah, Beis Hillel is concerned about 'Ta'aseh ve'Lo min he'Asuy' - but not about 'Gezeiras Tikrah'.

(b) The problem with Beis Shamai is - why should he require both forms of rectification? If he is concerned about 'Ta'aseh ve'Lo min he'Asuy' then either one should suffice; whereas if he is concerned about Gezeiras Tikrah, then removing every second plank should do the trick?

(c) In fact, Beis Shamai's concern is 'Gezeiras Tikrah' - and what they are really saying is that even shaking the planks will not suffice until one removes every second plank.

(d) That is indeed the opinion of Rebbi Meir, only Rebbi Meir maintains that his opinion is unanimous, and that even Beis Hillel subscribes to it.

(a) Rebbi Chiya bar Aba Amar Rebbi Yochanan, tries to establish the previous Mishnah (where Rebbi Yehudah permits a Sukah of planks and Rebbi Meir forbids it) by planks that are less than four Tefachim wide, but which have been smoothened. He does so in order to explain why Rebbi Meir and Rebbi Yehudah argue what appears to be the same Machlokes, twice.

(b) According to him, they argue over whether Chazal issued a decree, forbidding S'chach consisting of vessels that are *not* subject to Tum'ah (e.g. 'Peshutei K'lei Eitz' - straight wooden vessels that cannot receive liquids) because of vessels that *are* - Rebbi Meir holds that they *did*, Rebbi Meir, that they did *not*.

(c) We refute this explanation on the basis of Rav Yehudah Amar Rav, who (on Daf 12b) permitted male arrows, in spite of the possible decree forbidding them because of female arrows - and if they did not issue a decree *there*, why should they do so *here*?

(d) So we establish both Mishnah by Gezeiras Tikrah - the *first* Mishnah introduces the Machlokes, whereas in the *second*, Rebbi Yehudah comes to point out that 'Gezeiras Tikrah is the opinion of Beis Shamai, to which Rebbi Meir replies that in fact, it is unanimous.

5) One is permitted to use metal rods or bed-posts (that are subject to Tum'ah) to hold the S'chach - provided one leaves the equivalent space between them as the slats themselves.

6) Rav Papa permits 'Parutz ke'Omed' by the walls of Shabbos - meaning that if the spaces between the posts that form a wall were exactly the same as the posts themselves, the wall is Kasher regarding carrying on Shabbos. This only applies however, to posts and spaces of more that three Tefachim - because by spaces of less than that, we apply the principle of 'Levud', with which everyone agrees.

7)

(a) If, as Rav Huna Brei de'Rav Yehoshua maintains, 'Parutz ke'Omed' is forbidden by the walls of Shabbos - then why does the Tana of our Mishnah permit the S'chach, when it is exactly equal to the metal rods or the bed- posts?

(b) We answer this by establishing our Mishnah by 'Nichnas ve'Yotze' - which we understand to mean that it is impossible to measure the spaces *exactly* equivalent to the rods. If one expects the S'chach to fit between the rods, then one will inevitably leave slightly larger gaps than the rods themselves. On that, the Gemara asks 've'Ha Efshar le'Tzamtzem' (Why should it not be possible to measure the space exactly)?

(c) Rav Ami answers 'be'Ma'adif' - meaning that our Mishnah does not speak when he places the S'chach exactly in the middle, in the gaps, but when he also deliberately covers the rods too, in which case, there is a majority of S'chach.

(d) Rava answers the Kashya in a similar fashion - when one spreads the S'chach across the top of the rods, not parallel to them. By doing so, he cannot avoid placing more S'chach than rods, because, otherwise, it would fall through the gaps.

(a) Rav Ami bar Tivyumi invalidates a Sukah if the S'chach constitutes worn out vessels/clothes that are no longer fit for use (despite the fact that they are no longer subject to Tum'ah) - in case one comes to use them *before* they become unfit for use.

(b) His opinion cannot be borne out from our Mishnah, which clearly invalidates a Sukah whose S'chach constitutes bed-posts - because our Mishnah may be speaking in a case when the bed-posts is placed on the Sukah, together with the two legs still attached to it, and such a bedpost is still fit for use (and therefore subject to Tum'ah), as we shall soon see.