There is a comment regarding 10 Teves which seems to have passed into folk knowledge. The BH"G writes that if any fast were to fall on Shabbos, the issur of fasting on Shabbos would be doche the ta'anis. However, with respect to 10 Teves, since the ta'anis is stated in Nach as falling "b'etzem hayom hazeh" (Yechezkel 24, see R"H 18b), on the precise date of the 10th, even if that day were to occur on Shabbos one would be obligated to fast. How does the fact that the Navi specifically designates the day change 10 Teves from all other fasts where the day of the fast is also defined precisely by the halacha? In the Chiddushi HaGR"Ch (stencil), R' Chaim Soloveitchik explains that all the other fasts in Nach are referred to by the month they fall in - "tzom harevi'i, tzom hashevi'i...", etc. If those fasts were to fall on Shabbos, we can subsitute another day of the month for the day of Shabbos. However, with respect to 10 Teves, the date, not the month, defines the fast, and therefore there can be no substitute.
I thought perhaps with this chiddush of R' Chaim we could explain a difficult Tosfos in Megillah. The gemara has a hava amina that Rebbi wanted to abolish the fast of 9 Av, which Tosfos finds incredible because a latter Bais Din has no right to overrule a takkanah of an earlier Bais Din (in most circumstances), and 9 Av was established by the Nevi'im. Tosfos therefore suggests that the hava amina merely meant that Rebbi wanted to abolish the additional strictures of 9 Av beyond other fasts, or perhaps Rebbi wanted to change the date of 9 Av to 10 Av (see Tos as to why). Asks the RashaSh, but moving the date of a holiday or fast once established by Chazal is also uprooting a takkanah of Bais Din (see Megillah 2a)!? Based on R' Chaim's chiddush we can answer that the precise date of 9 Av was never established by the Bevi'im, only the month was established. Exactly which date of the month should be the fast day was left to Chazal's judgement.
Easy fast to all!!!