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Eruvin 94b - Pi tikra yored v'soseim from four sides

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According to Rashi:
Rav and Shmuel have an argument about an isolated אכסדרא; it has no walls, only a ceiling, but maybe you can carry in it because of פי תקרה יורד וסותם - the edge of the ceiling is considered to define a vertical barrier on each side. Shmuel holds that while you can sometimes say פי תקרה יורד וסותם (call it פתיו"ס), you can't do it for all four walls.

Now the number four seems funny to me: on three walls you can say it? So I would have liked to explain that "four walls" means, all around. You can say the principle, but only if you at least have some walls to start with.
Unfortunately, that's wrong: Rashi explains a case in the gemara very clearly not like that. You've got a house where two walls that meet in a corner are broken open, and part of the ceiling gone as well. The ceiling is broken back away from the wall in a zigzag shape. So if you want to say פתיו"ס, you need to do it four times, on four ceiling edges, over and up and over and up, so to speak (see the picture in Rashi). Rashi takes "four times" very literally. In fact, he also discusses a companion case where the ceiling is broken away from just one wall, where you only need פתיו"ס three times, over and across and back, and he says that Shmuel would agree on that.

Why four? Maybe Shmuel argues even on two or three, and the case of אכסדרא only uses four to illustrate כחו של רב? Is there some way to explain why four should be different from three?

I'm not sure this question will bother most people: that's what Shmuel holds. But doesn't Shmuel have to have some way of distinguishing three from four in his mind in order that he could have come up with this din?

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