The Mishna in the second chapter of Masekhet Sukka (25a) establishes the well-known rule that it is permissible on Sukkot to eat “arai” – a small amount – outside the sukka. The Shulchan Arukh (O.C. 639:2) rules that this refers to a quantity of bread up to a ke-beitza (the volume of an egg).
The Shibolei Ha-leket (344) cites a fascinating ruling in the name of Rabbeinu Avigor, imposing a very significant qualification on this exemption, namely, that it does not apply on Shabbat or Yom Tov. If one eats even small amounts on the first day of Sukkot (or first two days in the Diaspora), or on Shabbat during Sukkot, then the food must be eaten in the sukka. This ruling is based upon the principle established by the Gemara in Masekhet Beitza (34b) that even a small snack eaten on Shabbat is treated as a meal with respect to the laws of ma’aser (tithing). As the Gemara there discusses, if one has produce which he plans on bringing into his home, he may eat small amounts before bringing it into his home without separating the required tithes. Although he may not eat a meal from this produce, he is allowed to eat small amounts at this point. However, the Gemara states that on Shabbat, the consumption of even small amounts constitutes a “meal,” insofar as it fulfills one’s obligation of oneg Shabbat (enjoying oneself on Shabbat), and thus such produce may not be eaten in any amounts on Shabbat if the tithes have not been separated. Rabbeinu Avigdor contended that this provision is relevant to the obligation of sukka, as well. The consumption of even small amounts of food on Shabbat – and Yom Tov – qualifies as “akhilat keva” – eating a “meal” – and thus requires a sukka. Therefore, in his view, it is only on the weekdays of Sukkot that Halakha permits eating small amounts outside the sukka.
Several later writers challenged Rabbeinu Avigdor’s theory in light of the next Mishna in Masekhet Sukka (26b), which tells of two rabbis who were once brought small amounts of food and made a point of eating the food in the sukka. The Gemara explains that this story was told to instruct that although one is permitted to eat small amounts of food outside the sukka, it is legitimate for a person to act stringently and avoid eating any quantity of food outside the sukka. (Meaning, adopting such a measure is deemed appropriate and admirable, and not an arrogant display of misplaced piety.) According to Rabbeinu Avigdor, we might wonder how the Gemara reached such a conclusion. After all, it is possible that this incident occurred on Shabbat, or on Yom Tov, and it was for this reason that these sages insisted on eating the small amounts of food in the sukka. The fact that the Gemara did not consider this possibility would seem to prove that no distinction exists in this regard between the different days of Sukkot, and even on Shabbat and Yom Tov, small amounts of food may be eaten outside the sukka. Indeed, the Elya Rabba (639:1) contends that the halakhic authorities generally ignored Rabbeinu Avigdor’s ruling because it is disproved by the Gemara’s discussion. (Others, however, suggested ways of defending Rabbeinu Avigdor’s position. See, for example, the Chida’s discussion in Birkei Yosef, 639:5.)