Pesachim 112b relates a story about demons. The queen of demons (with a large army) used to be permitted to wreak havoc at will (which is a separate question), until one day when she encountered R. Chanina b. Dosa. She told him that they spoke of him in heaven and told her of his learning, so she was not allowed to take action against him. He availed himself of this opportunity to forbid her to travel through settled areas, but when she pled for mercy he relented and said she could come out on two nights, Tuesday night and Shabbat (Friday night).

Why those particular nights? Shabbat in particular seems like a peculiar choice to me; it seems like a time that we would want to minimize, not maximize risk, since it is a social evening. And Tuesday night just seems random. Furthermore, it seems rather odd that he would give her two nights, and not just one, or even that he would relent at all. Is there something we're supposed to learn about those nights from this episode?

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    "dinner guests who then walk home" I think this is an anachronism. Everyone then walked everywhere and I doubt there was as much mutual meal hosting as there is in today's American Jewish culture. – Double AA Oct 10 '13 at 16:22
  • Indeed, @DoubleAA, Friday night is supposed to be an especially good time for rain, since people are home (Rashi on Vayikra 26:4 , cited here with additional insight by R' Frand). Maybe this selection is related. – Isaac Moses Oct 10 '13 at 16:27
  • It'd probably be worth checking to see if the Maharsha has any commentary to offer on this. – Isaac Moses Oct 10 '13 at 16:37
  • Aww, you stole my question! Actually, I believe it's Tuesday night, not Wednesday night (it's Wednesday Eve, IINM). – Seth J Oct 10 '13 at 16:46
  • Actually, my question was why allow her two nights, why not just one, or why not once a year, or why not one hour, etc. – Seth J Oct 10 '13 at 16:47