(Please forgive the delay in response. Technical problems prevented the mailing of a number of responses.)

Daniel, it is very good to hear from you again!

1) The simple answer to your question would seem to be that Rebbi Yehudah is consistent with his opinion here (10b) that a Sukah must be a "Diras Keva" -- a permanent dwelling.

2) See the Gemara in Sukah 7b, which cites a number of opinions among the Tannaim who also maintain that a Sukah should be a Diras Keva. One of these opinions is that of Rebbi. The proof that Abaye provides there in the Gemara for his assertion that Rebbi requires a Diras Keva is the fact that Rebbi said in a Beraisa that a Sukah smaller than 4 by 4 Amos is invalid. Therefore, it seems reasonable to assume that Rebbi Yehudah also maintains that the minimum size for a Sukah is 4 by 4 Amos, and therefore it is big enough to require a Mezuzah.

3) However, this is not so simple, because the Mishnah in Sukah (2a) states that Rebbi Yehudah permits a Sukah higher than 20 Amos. The Gemara there (Sukah 7b) states that this is because according to Rebbi Yehudah a Sukah should be a Diras Keva. The Rosh (beginning of Sukah) writes that this means that Rebbi Yehudah maintains that a Diras Keva is also valid. The Tosfos ha'Rosh (Sukah 7b, DH Kulhu) explains further that Rebbi Yehudah does not actually require that it should be specifically a Diras Keva, but rather that if it is a Diras Keva, it is acceptable, and therefore if it is over 20 Amos it is valid. According to this, it appears that if the Sukah is less than 4 by 4 Amos, Rebbi Yehudah could agree that it is valid.

4) Accordingly, we will have to say that when the Gemara here (Yoma 10a) states that according to Rebbi Yehudah a Sukah requires a Mezuzah, this refers only to a Sukah which is 4 by 4 Amos or larger, even though a Sukah does not necesarily have to be that large according to Rebbi Yehudah.

5) However, the Ramban (in Milchamos Hash-m to Sukah, page 1b of the pages of the Rif printed with the Rif Sukah 1b (in Rif pages) seems to disagree with the Rosh because he writes that Rebbi Yehudah invalidates a Diras Arai, a temporary dwelling. Since Rebbi Yehudah requires specifically a Diras Keva, it would seem that a Sukah smaller than 4 by 4 Amos is Pasul. Therefore, according to the Ramban, we may remain with the answer we gave to your question above in (1) and (2).

6) In summary, the simple answer to your question is that Rebbi Yehudah maintains that the smallest possible Sukah is 4 by 4 Amos because he requires a Diras Keva. However, even if one says that a Sukah smaller than 4 x 4 Amos is also valid according to Rebbi Yehudah, we may say that when the Gemara here says that Rebbi Yehudah requires a Mezuzah for a Sukah, this refers only to a Sukah which is 4 by 4 Amos or larger.

7) Incidentally, you wrote that the minimal Sukah is 1.5 Amos by 1.5 Amos. In fact, since there are 6 Tefachim in one Amah, this means that an Amah and a half is 9 Tefachim, while the minimum size of a Sukah is 7 Tefachim.

Dovid Bloom

Here is a different answer to your question, which seems rather surprising at first sight.

1) This is based on the Talmud Yerushalmi near the beginning of Maseches Sukah 1:1 (page 3a in the standard editions) (this also appears in the Yerushalmi Ma'aseros, on the Mishnah in Maseches Ma'aseros 3:7 which is cited by the Gemara Bavli in Yoma, end of 10a). According to the text of the Korban ha'Edah, this reads that Rabbi Yehudah said that even a Sukah that does not possess 4 walls, or is not 4 by 4 Amos, is valid. The Yerushalmi continues (and this part conforms also with our text): "And so did Rabbi Yehudah require a Mezuzah for a Sukah even though it has neither 4 Amos or 4 walls." The Korban ha'Edah writes that according to Rebbi Yehudah, any kind of Diras Keva for a Sukah is sufficient, which is why he does not require 4 Amos, and in addition he requires the affixing of a Mezuzah even if the Sukah is less than 4 Amos.

2) This would seem to be exactly the opposite of what logic would demand. The Halachah says that one must affix a Mezuzah only if the house is 4 by 4, but now we learn that Rebbi Yehudah says that for a Sukah one does not require 4 by 4. In addition, Rebbi Yehudah says that the reason is because a Sukah is a permanent dwelling. But if it is less than 4 by 4, does that not mean that it could not be a permanent dwelling?!

3) We can answer this paradox with an idea said by Rav Elyashiv zt'l (in He'oros b'Maseches Sukah to Daf 3a, DH uv'Derech). The Rabanan, who disagree with Rebbi Yehudah, maintain that a permanent dwelling is invalid as a Sukah. Therefore, according to the Rabanan, one cannot say that a Sukah is permanent because the Torah wants us to dwell in a temporary structure on Sukos. However, Rebbi Yehudah maintains that a permanent dwelling is also in order on Sukos. This means that when the Torah commands us to dwell on Sukos in a Sukah, a Sukah is automatically considered as permanent. Rav Elyashiv said "Achshevei k'Diras Keva" -- the Torah gave to a Sukah the importance of a permanent dwelling. It follows that every Sukah, even though in physical reality it is a temporary dwelling, nevertheless because of the command of the Torah to live in it on Sukos it becomes a permanent dwelling. This is why Rebbi Yehudah maintains (Yoma 10a) that a Sukah on Sukos requires a Mezuzah; on Sukos it is transformed by the Torah into a permanent home.

4) According to this, we can understand why a Sukah needs a Mezuzah on Sukos according to Rebbi Yehudah even though it is only 7 by 7 Tefachim. Since the Torah says that a 7 by 7 Sukah on Sukos is valid, it follows that this is a permanent dwelling on Sukos. The rest of the year it does not require a Mezuzah, but, on Sukos, the Torah says that if a Sukah is Kosher it is automatically a permanent home. If so, it requires a Mezuzah. (See also He'oros b'Maseches Sukah 8b, DH A'R.)

5) I posed your question to a Gadol and he replied "Mitzvah Machshivato" -- the Mitzvah of Sukah gives an importance to the Sukah and consequently it requires a Mezuzah even though it is smaller than 4 by 4 Amos. This actually seems quite similar to the answer I cited above in the name of Rav Elyashiv.

What this seems to suggest is that what determines whether a house or room needs a Mezuzah is not necesarily whether it is 4 by 4 Amos but rather a more basic factor. The crucial question is whether the room is "Chashuv," important. In most cases a room is not important if it is smaller than 4 by 4, but there are some exceptions to this rule:

a) There is the example of "Burganin, huts on the edge of the city. They are considered as houses and are able to extend the distance that one is allowed to walk out of the city on Shabbos. The Gemara in Sukah (3b) states that the reason is that they are "Chazi l'Milsaihu" -- capable of fulfilling their purpose (that somebody can sleep there overnight). The Ritva there writes that even though it is smaller than 4 by 4 Amos, it is still considered a house.

b) The Rashash (Sukah 3b) writes that we learn from this Gemara that the entrance to a house requires a Mezuzah even though it is smaller than 4 by 4 Amis because it has a specific purpose which gives it importance. He cites the Piskei Teshuvah (Shulchan Aruch, Yoreh Deah 286:11) who rules that if a big house contains smaller rooms of less than 4 by 4 Amos where the owner places items, these require a Mezuzah even though they are smaller than 4 by 4, since they have a specific purpose.

Kol Tuv,

Dovid Bloom