Bavli P'sachim 112:2 has a story of an angel of destruction who would work daily (see Rashash) until asked to quit. When she requested some time to work, the rabbi she was talking with allowed her Tuesday and Friday nights: the g'mara warns us, therefore, not to go out alone Tuesday and Friday nights. (This is more famous, I think, from the Rashi at the start of B'chukosay.)
Obviously, this g'mara needs to be understood on an appropriate level, and there are some obvious, major questions one can ask on it (such as "why did the rabbi accede to her request?"). But I have one minor question: why those nights specifically? (Someone once told me that those are nights that people didn't tend to be out anyway: market days were Mondays and Thursdays, so people would travel to and from the cities on Sunday, Monday, Wednesday, and Thursday nights. But what about Saturday nights (motzae shabasos)?)
Of course, maybe a fuller understanding of the whole agada would render this question moot, as it would make the reason for Tuesday and Friday nights obvious, but I don't have such an understanding. (Such is most welcome as a response to this question. Maharsha and Ben Y'hoyada both say nothing.)
