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1)

(a) Why does the Tana need to add the case of 'Ribah le'Echad, u'Mi'at le'Echad', which appears to duplicate the previous Halachah?

(b) Abaye limits the discrepancy (in the previous case) between the two corners of the same side, to the difference between the diameter of a circular and the diagonal of the square, but not more.
Why is that?

(c) Our Mishnah quotes Chazal, who say that by all matters of Eruv, we take the lenient view.
Then how will we explain the Beraisa 'Lo Amru Chachamim es ha'Davar Lehakel Ela Lehachmir'?

(a) Ir shel Yachid ve'Na'asah shel Rabim, Me'arvin es Kulah.
What is the criterion for including the whole town in the one Eruv?

(b) Do the Mavu'os then also require individual Eruvin?

(c) Are we speaking here, about a town with or without a real Reshus ha'Rabim?

(d) Why, in the reverse case (Ir shel Rabim ve'Na'asah shel Yachid) are they not permitted to make a communal Eruv on behalf of the whole town (unless that is, certain conditions are met)?

4)

(a) Why does the Gemara initially think that an Ir shel Yachid ve'Na'aseh shel Rabim must have previously belonged specifically to the Resh Galusa?

(b) On what grounds does the Gemara reject that contention?

(c) How does one rectify an Ir shel Yachid ve'Na'aseh shel Rabim, if a Reshus ha'Rabim passes through it?

(d) Why can one not do the same with an Ir shel Rabim which always was an Ir shel Rabim?

(a) What are two alternative ways of being Me'arev an Ir shel Yachid ve'Na'aseh shel Rabim? Why can half the town not make a communal Eruv, and the other half, Mavoy by Mavoy?

(b) Under which condition may an Ir shel Rabim that was always an Ir shel Rabim combine the whole town in one Eruv?

(c) Who is the author of this Beraisa, which permits making an Eruv in a Reshus ha'Rabim?

(d) An Ir shel Yachid ve'Na'asis shel Rabim is permitted to be Me'arev Mavoy by Mavoy, but not to divide the town into two, to make two Eruvin.
Why is this?

6)

(a) How does Rav Papa qualify the prohibition of the Mavu'os of an Ir shel Yachid ve'Na'asis shel Rabim being Me'arev independently?

(b) The Gemara suggests that this statement does not go like Rebbi Akiva, who says (in Perek ha'Dar) 'Regel ha'Muteres bi'Mekomah, Oseres Afilu she'Lo bi'Mekomah.
What does this mean?

(c) How does the Gemara establish Rav Papa even like Rebbi Akiva?

(d) According to the second Lashon, Rav Papa maintains that the Mavu'os are not even permitted to be Me'arev seperately width-ways.
How can this go even like the Chachamim, who hold 'Reshus ha'Materes bi'Mekomah, Einah Oseres she'Lo bi'Mekomah'?

(a) For the same reason that the town is not permitted to divide into two, to make two Eruvin (see 5d), it should also be forbidden to divide into separate Mavu'os - even with a Lechi or a Koreh.
Why then, does the Beraisa permit it?

(b) What is a 'Dakah', and what purpose does it serve?

(c) The concept of Dakah comes from Rav Chisda.
In what connection did *he* teach it?

(a) Why did Rebbi Zeira think that it was in order to be'Me'arev the town in which Rebbi Chiya lived, without leaving a 'Shiyur'?

(b) What was Rebbi Chiya bar Asi's real reason for being Me'arev the town, and why was it no longer applicable?

(c) What was Rebbi Zeira's reaction, when Abaye told him this?

(a) What is the difference whether a ladder serves as a Mechitzah or as an entrance?

(b) Rabah quoted Rav as saying that a ladder (where it serves as the only entrance between two towns) is considered an entrance. Rav Nachman claimed that *that* was not what Rav actually said.
What *did* Rav say?

(c) What does he say about a ladder between two courtyards?

(a) What does Rav Nachman rule with regard to a Chatzer and an upstairs (outside) balcony with a ladder leading down to the Chatzer who forgot to make a joint Eruv?

(b) How does that appear to clash with Rav Nachman's opinion quoted in the previous question?

(c) How do we reconcile the two?

(d) If the balcony is less than ten Tefachim high, then how can the 'Dakah' be effective?