Sanhedrin 13: Intercalation, Smicha of Judges

The Gemara looks into intercalation in great detail.  By which date must it be decided that the calendar will be adjusted?  Considering the months of Tamuz and Tishrei, how far into Tishrei is "the majority" of the month?  16 days or 21 days?  The rabbis walk through numerous calculations and considerations as they work with the math and the implications of moving the new tefuka.  And when does the tefuka end and then begin?  How much should the Festival dates be considered a critical part of this discussion?  Their conversation is long, detailed, somewhat difficult to follow, and very thoughtful.

The rabbis then consider how many judges are required to grant smicha to other judges.  It was understood that three judges were needed, but the rabbis cannot find a proper proof text for this custom.  In their search for the origin of this practice, the rabbis find proofs for other possible numbers of judges.  

At the end of today's daf, the Gemara considers how smicha is performed.  We learned that there was a "laying of hands".  Was that actually a required part of the practice?  After debating this custom, Rav Ashi answers that laying of hands is not required.  Instead, the new judge is offered the title of "Rebbi" and he is given permission to judge regarding fines.