1) HOUSES AND COURTYARDS OPENING INTO A MAVOY
OPINIONS: Rav Nachman rules that the only type of Mavoy in which a Lechi or Korah permits one to carry is a Mavoy into which houses and Chatzeros open. The MISHNAH BERURAH (OC 363:102) cites the BEIS YOSEF in the name of the RASHBA who explains that the Rabanan required that in order to be able to carry in a Mavoy with a Lechi or Korah, the Mavoy must be an area used by many people who will point out to each other the Lechi or Korah. That is why an adjustment as small as a Lechi or Korah suffices to permit one to carry in the Mavoy. A Chatzer, though, which is not used by as many people as a Mavoy, requires a larger adjustment (a Pas at least four Tefachim wide, or two Lechayayim) in order to permit one to carry in it. (See also TOSFOS DH u'Vatim.)
How many houses and courtyards must open into the Mavoy so that a Lechi or Korah suffices and permits one to carry in the Mavoy?
(a) The RAMBAM (Hilchos Shabbos 17:8) writes that a Lechi does not suffice for a Mavoy that "has only one house or one Chatzer." The RASHBA infers from these words that the Rambam maintains that even one Chatzer with one house suffices. This is the opinion of Shmuel in the Gemara later (Eruvin 72b). However, this is contrary to the opinion cited as the Halachah by the Gemara here, and, according to the conclusion of the Gemara later (72b), even Shmuel may agree that a Lechi does not suffice for a Mavoy that has only one Chatzer with one house.
(b) RASHI (DH u'Vatim v'Chatzeros) explains that there must be two Chatzeros which open into the Mavoy, and each Chatzer must have at least one house which opens into it. This is also the opinion of the RA'AVAD (cited by the Rashba).
(c) The RASHBA strongly disagrees and requires that each of the two Chatzeros have two houses which open into it. This is also the opinion of Rashi elsewhere (Shabbos 130b, Eruvin 74a), and this is the opinion of most of the Rishonim.
HALACHAH: The SHULCHAN ARUCH (OC 363:26) rules that a Mavoy requires two houses in each of two Chatzeros, in accordance with the view of the Rashba and most Rishonim.