1)

(a)The Torah refers to the Tefilah of a Tzadik as a pitch-fork - in connection with Yitzchak's Tefilah (in Toldos), where the words "v'Ye'tar" and "va'Ye'aser" are used, in place of more common expressions of Tefilah.

(b)This teaches us - that the Tefilah of a Tzadik, acts like a pitchfork, turning Hash-m's Midas ha'Din into Midas ha'Rachamim.

2)

(a)Rebbi Yehudah permits the use of planks as Sechach. Rebbi Meir forbids it.

(b)A plank of four Tefachim ...

1. ... invalidates the Sukah if it is in the middle of the Sukah, but not if it is ...

2. ... adjacent to the wall of the Sukah.

(c)The Mishnah nevertheless - forbids sleeping underneath the latter.

3)

(a)According to Rav, Rebbi Meir and Rebbi Yehudah argue over a plank that is at least four Tefachim wide - because that is the width of most planks that form a ceiling, and we are afraid that one might go on to make one's Sukah in the house, using the ceiling as Sechach.

(b)They did not decree by planks of less than four Tefachim - because it is unusual for such narrow planks to comprise a ceiling.

4)

(a)Shmuel establishes the Machlokes by planks that are less than four Tefachim wide. According to him ...

1. ... Rebbi Meir holds that Chazal even decreed by narrow planks of between three and four Tefachim - because of the minority of people who make their ceilings like that (and we find in other places too, that Rebbi Meir follows the minority).

2. ... Rebbi Yehudah holds like both he and Rebbi Meir held according to Rav (as we explained earlier).

(b)Shmuel will hold by planks that are four Tefachim wide or more - that the Sukah is Pasul, even according to Rebbi Yehudah.

5)

(a)The problem with Shmuel, who establishes the Machlokes by planks that are less than four Tefachim is - that this seems to include planks of even less than three Tefachim, which are really no more than canes (and which ought to be permitted).

(b)Rav Papa resolves the problem - by adding to Shmuel's ruling that planks of less than four Tefachim are Kasher even according to R. Meir.

(c)According to Rav, the problem with our Mishnah, which forbids sleeping underneath a plank of four Tefachim is - that, according to R. Yehudah, who does not differentiate between a plank of more than four and one that is less, this ought not to be the case!?

(d)And we resolve it - by establishing our Mishnah like Rebbi Meir.

6)

(a)The Tana Kama in a Beraisa invalidates two sheets placed next to each other, as if they were one, but not two planks; Rebbi Meir invalidates two planks just like two sheets. Shmuel establishes this Beraisa by two planks that make up four Tefachim - the Tana Kama is Rebbi Yehudah.

(b)Shmuel will explain the Machlokes as he explained earlier - that Rebbi Yehudah does not hold of Gezeiras Tikrah, even by one plank that is more than three Tefachim, and certainly not by two; whereas Rebbi Meir (who permits one plank that is more than three Tefachim) forbids two planks that total four Tefachim or more.

(c)The problem with Rav (in whose opinion Rebbi Meir and Rebbi Yehudah argue about a plank of four Tefachim, but not less) is - that 'Mah Nafshach', if the Tana is speaking about planks of four Tefachim, then why does Rebbi Meir require two planks to invalidate the Sukah? Whereas if we are speaking about planks of less than four Tefachim - then two planks ought not to invalidate the Sukah, even according to him, seeing as, in Rav's opinion, planks of less than four Tefachim are no different than canes.

(d)Rav establishes the Machlokes by planks that are placed next to the wall - where Rebbi Yehudah permits even sufficient planks to make up four Amos; even though 'Dofen Akumah' no longer applies at that point, nevertheless, he validates the Sukah, because planks of four Tefachim are Kasher; whereas Rebbi Meir validates the Sukah only as long as the planks of four Tefachim do not total four Amos.

7)

(a)According to the second Lashon, it is Shmuel who explains the 'Mitztarfin' of Rebbi Meir to refer to four Amos. According to this Lashon - Rebbi Meir will not invalidate the Sukah, even if, in the middle of the Sukah, there are two planks of three Tefachim each, despite the fact that together, they total more than four Tefachim.

(b)Rebbi Yehudah's reason, according to Shmuel - is exactly as we explained it in the previous answer according to Rav (i.e. because, since he does not hold of Gezeiras Tikrah, he even permits the entire roof of the Sukah to be formed of planks of three Tefachim).

(c)Rav will learn Rebbi Meir in exactly the same way as Shmuel. According to him, Rebbi Yehudah says 'Shnei Nesarim Ein Mitztarfin' - only to counter Rebbi Meir, who says 'Mitztarfin'.

8)

(a)One Beraisa supports Rav, another Beraisa supports Shmuel. In the first Beraisa, Rebbi Yehudah brings a proof for his opinion (that planks of four Tefachim are Kasher) - from a certain occasion when, in time of danger (due to the decrees issued by the Romans' forbidding the performing of Mitzvos), instead of regular Sechach, they escaped detection by using planks of four Tefachim, which they placed on the roof of a balcony, to form a Sukah.

(b)The Rabanan refute this proof - on the grounds that what was permitted in times of danger is not necessarily permitted on a regular basis. (Note: Presumably however, they did not recite a Berachah).

(c)In the second Beraisa, Rebbi Meir concedes that the Sukah is Kasher even if there are planks of three (or even four) Tefachim on the Sukah - provided the spaces between the planks are equal to the planks. We shall see later, that he is speaking about a Sukah that is exactly eight by eight Amos, and that 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 Sechach). This comprises a Sukah with 'bent walls' of less than four Amos, which is Kasher.

(d)According to Shmuel, Rebbi Yehudah concedes that planks of four Tefachim wide will invalidate the Sukah - in which case, we would have had to establish the Beraisa in exactly the same way as Rav. However, the Tana chose to inform us that the Sukah will be Kasher according to Rebbi Meir, to teach us that even Rebbi Meir, who is more stringent than Rebbi Yehudah in this regard, will validate a Sukah that is made in this way.

9)

(a)In the same Beraisa, Rebbi Yehudah concedes to Rebbi Meir - that, although a plank of four Tefachim adjacent to the wall does not invalidate the Sukah, one should nevertheless not sleep underneath it, and somebody who did has not fulfilled the Mitzvah of Sukah.

10)

(a)Rav Chisda and Rabah bar Rav Huna thought that - planks of four Tefachim wide but less than four Tefachim thick that are placed on their sides, do not invalidate the Sukah.

(b)They hoped that Rav Nachman who came to visit Sura, would support them, but he didn't. He agreed with Rav Huna - who rules that they do.

11)

(a)The Beraisa invalidates a Sukah that cannot fit a person's head, most of him and his table - the equivalent of seven Tefachim (six for him and his head, and one for his table).

(b)The Tana also invalidates a Sukah, if a gap in the bottom of the wall is large enough to allow a kid-goat to enter easily - the equivalent of a three Tefachim gap (up to three Tefachim we apply the principle of 'La'vud').

(c)We attempt to prove Rav Huna right from the same Beraisa, which invalidates a Sukah which has a plank that is four Tefachim wide, but which only takes up three Tefachim in the Sukah - which we initially think refers to Rav Huna's case (of a plank that is four Tefachim wide and three Tefachim thick standing on its side.

(d)But we reject this proof by establishing the Beraisa by 'Pesel ha'Yotzei min ha'Sukah' ...

1. ... (Sechach that protrudes beyond the confines of the walls) ...

2. ... meaning that if, by a Sukah consisting of three walls, one placed a plank of four Tefachim across the Sukah at the end where there is no wall, with three Tefachim covering the two opposite walls, and the fourth Tefach protruding beyond that (covering an area where there are no walls at all) the plank nevertheless invalidates the entire Sukah, because of 'Pesel ha'Yotzei min ha'Sukah' (which is considered part of the Sukah).