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1)

(a) Rachbah asked his Talmidim what the Din would be if there were two courtyards, one at either end of the two adjoining houses, each with a house at the far end, and the residents of each courtyard wished to make an independent Eruv to carry in their courtyard. To do this, they wished to place their respective Eruvin in the other house (that did *not* adjoin their courtyard, treating the adjoining house that *did*, as a Beis-Sha'ar.
What did they answer?

(b) What does Rava say about two individual people who asked someone to place two Eruvin for them, which he did, one when it was still day, the other during Bein Hashemashos, if the first one was eaten during Bein Hashemashos, and the second one after nightfall?

(c) What is Rava's big Chidush, and what problem does it present the Talmidim of Rachbah?

(d) What is the basic difference between the two cases?

2)

(a) Where must a window in a wall between two courtyards be placed to enable them to make a joint Eruv, and what must its minimum dimensions be?

(b) Why is a window that is higher than ten Tefachim not considered a Pesach in this regard?

(a) Is the Din of four by four Tefachim in our Mishnah connected to the Din of Levud?

(b) If it had been, who would have to be the author of our Mishnah?

(c) Having informed us that the window must be within ten Tefachim of the ground, why does the Mishnah then see fit to add that if it above ten Tefachim, it is invalid?

(d) Having already taught us that a window which is mostly above ten Tefachim is still valid, why does the Beraisa need to then add that if it is mostly within ten Tefachim, it is also valid?

(a) Rebbi Yochanan states that a circular window must have a circumference of twenty-four Tefachim.
Why is that?

(b) And why does he say that at least two Tefachim and a Mashehu must be within ten Tefachim from the ground?

5)

(a) How much more is ...

1. ... the circumference of a circle than its diameter?
2. ... the area of a square than the circumference of the circle that contains it?
3. ... the diagonal of a square more than one of its sides?

(b) What then ought the circumference of Rebbi Yochanan's circular window to be?

(c) So why does Rebbi Yochanan require twenty-four Tefachim?

(a) The ruling of our Mishnah (that a window in a wall above the height of ten Tefachim is invalid as regards Eruv) does not apply to a wall in between two houses, says Rav Nachman.
Why not?

(b) How does Rav Nachman explain the Beraisa, which writes that whether a window is between two courtyards, two houses, two attics, two roofs or two rooms, it needs to be four by four Tefachim and within ten Tefachim?

(c) Who must be the author of this Beraisa (which requires an Eruv for two roofs)?

(a) Rav Aba asked Rav Nachman whether a skylight (that leads to the attic belonging to a second person) in the middle of the ceiling, requires a fixed ladder or not? What is the Sha'aleh, and why might it need one?

(b) Rav Nachman replied that it does not in fact, require a *fixed* ladder.
Does it require a ladder at all?

(a) Is it possible for two houses whose garden or courtyard is divided by a wall of ten Tefachim to make a combined Eruv?

(b) Why does the Mishnah add that the wall is four Tefachim wide? Is that because otherwise, it would not be considered a wall to divide between two courtyards?

(c) May one use the wall to transfer food etc. from one courtyard to the other?

(a) How wide would a breach in the wall need to be in order to retain the right to make an independent Eruv, and why is this?

(b) What will be the Din if, in the case when the breach is more than ten Amos, the residents of each Chatzer make an independent Eruv? Are their respective Eruvin valid?

(a) According to Rav, if the wall is less than four Tefachim wide, the top may not be used by either Chatzer.
Why not?

(b) What does Rebbi Yochanan hold?