Siman 379

Two courtyards with three houses between them, this house open to this courtyard and this house to that courtyard, and the middle house open to the two houses from here and from there, and they wish to make an eruv together; the resident of this courtyard comes by way of the house open to him and places his eruv in the middle one, and treats the house open to him as a gatehouse to pass through it to the middle one, and likewise the resident of the other courtyard treats the house open to him as a gatehouse and they made an eruv in the middle one—none of the three houses needs to give bread. These two outer ones—because of the status of a gatehouse, and the middle one—because a house in which an eruv is placed does not need to give bread; so it is in the Gemara. (End of the chapter 'Hadar' and in the Tur and Shulchan Aruch)

And it is not understood, for if so, there is no need for an eruv at all, and how would they join together without an eruv? Rather, this is the explanation: that there are many houses in the courtyards, and all of them placed their eruv in this middle one, and therefore these three do not need to provide an eruv. And so it is explained from the words of the Rambam, chapter 4, law 10, who wrote: "Two courtyards with three houses between them... and the residents of this courtyard brought their eruv through the house open to them and placed it in the middle house, and likewise the residents of the other courtyard... those three do not need to provide bread, etc." Thus far his words, and the wording of the Tur and Shulchan Aruch is a concise wording. (And so wrote the Ritva)

And there are some who say that even if they placed their eruv in one of the other houses of the courtyard, these three do not need to provide bread. For example, when the residents of one courtyard, when they bring their eruv to the other courtyard and are forced to go through these three houses—they are all considered like a beit shaar. (Tosafot ibid.) And it appears to me that this is when they have no other path besides these three houses, but if they have another path—why should they be considered like a beit shaar? Therefore, they too must provide bread.

And know, that regarding every house that is a beit shaar as has been explained, however, one may not consider this one a beit shaar and that one a house. For example, two courtyards with two houses between them, and they did not make an eruv together but rather each one for itself, and a member of this courtyard came through the house that is next to him and placed his eruv in the house that is next to the second one, and the second one did likewise, in that he also placed his eruv in the house adjacent to the other courtyard—they have not acquired an eruv. For whichever way you look at it: if we consider each house as a beit shaar—behold, one who places his eruv in a beit shaar, it is not an eruv; and if we consider them as houses—behold, there is the interruption of a house between the courtyard and the house in which they place the eruv. Rather, you must say that for this one we consider his house that is next to him as a beit shaar and the second house as a complete house, and for the second one the opposite; if so, it is a contradiction between two opposites. And even though regarding eruvin we sometimes say even a contradiction between two opposites, as will be explained in siman 393, this is in a matter that is not so noticeable, but in a noticeable matter—it is like mockery and jest, and we do not give the Sadducees an opening to dominate. (Rashi, end of Perek HaHadar (Eruvin 76a))

And know, that regarding the laws that were explained in the previous simanim, that a foot forbidden in its own place forbids in a place not its own—there is room to investigate: if so, in a city that is entirely joined by an eruv like our cities, and people who dwell outside the city where the eruv does not encompass them come to the synagogue—why should they not forbid the entire eruv to us, like a foot forbidden in its own place that forbids in a place not its own? For this is not a comparison; specifically regarding an inner courtyard that has no opening except through the outer one is it relevant to say this, since he has no other place from which to exit to the public domain or to a mavoi. But here, behold the entire land is before them, aside from the city joined by an eruv which is like a large courtyard. And if it is because their desire is to go to pray in the synagogue, and perhaps they even have seats in the synagogue—what is it to us and their desire, for they are to us like mere guests. (See Sha'arei Teshuva in siman 378 what he wrote in the name of the Noda Biyehuda, second edition, Orach Chaim siman 44, and the responsa of Chinuch Beit Yehuda, and they agreed to permit it)