(a) Regarding the Ger at the end of the page -
1.a gentile was walking past the REAR of a study hall... why does the Gemara trouble itself to specify the 'rear'?
2. how was it that he was able to address the class with his questions?
3. how was the Gemara able to record what the gentile said 'to himself'?
4. what kind of a person might this gentile have been?
(b) Also, in regard to an earlier part (of Daf 31), when a gentile asks to be taught the entire Torah while standing on one foot... might this 'one foot' refer to the fact that only one of the gentile's parents was Jewish?
brian baderman, London UK
(a) About the Ger who wanted to be a Kohen Gadol -
1. The doors to the Batei Midrash (and Batei Kneset) were generally in the back of the room, opposite the Aron Kodesh (Berachos 6b Rashi DH Achorei). The Nochri heard what was being said in the study hall through the open doorway.
2. The Nochri's curiosity was piqued, so he entered and questioned one of the students. When asked, the student was compelled to tell the truth (as Yam Shel Shlomo writes regarding another Gemara, in Bava Kama 38a).
3. The Gemara inferred the Nochri's thoughts from the end of the story (according to the rule "Sof Ma'aseh b'Machashavah Techilah").
4. The Nochri was a sincere but simple gentile who was always curious about Judaism. That is why Hillel was certain that he would want to convert even after discovering that he cannot be a Kohen Gadol. (Tosfos Yevamos 24b DH Lo and 109b DH Ra'ah).
(b) I don't think so. If the mother was Jewish, he would not be called a "Nochri." If his father was Jewish, it would not help him at all and it should not have been considered even "one foot" to stand upon. The Nochri would have to make a full conversion (Yevamos 23a).
See the Maharsha here for an allegorical interpretation of the "one foot" of the Ger.