Who knows ninety-six?
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Yirmiyahu (52:23) describes the ornamentation of the columns Yachin and Boaz in the first Beis Hamikdash (which were destroyed by the Babylonians): "The pomegranates were 96 to the outside; all the pomegranates were 100 on the net all around."
The commentaries explain that there were actually 100 per column, but only 96 of them were visible, because the other four were embedded into the facade of the building. R' Yosei (Tosefta Ohalos 7:13) uses this to derive a general geometric principle: when a cylinder is tangent to a plane (e.g., a beam lying on the ground), 1/25 of its circumference will be hidden from view.
We fast ninety-six shaos z'maniyos (halachic hours) over the course of a year: twelve each on four fast days and twenty-four each on two. (This excludes "extra" time: between sunset and nightfall, and tosefes yom hakipurim. It also excludes taanis b'choros and other fasts that are not widely kept.)