Sanhedrin 3: Prooftexts and Opinions Regarding Numbers of Judges

Yesterday's daf taught us when three, five, nine, twenty-three, and seventy-one judges should hear a case.  The rabbis argue about why all cases are not investigated and tried in the same way when we are told in Leviticus (24:22) that we should have only one manner of law.  We learn that there is a concern about the qualifications of a judge.  People would have to be compensated for their losses after a ruling that was deemed to be incorrect.  

The Gemara then debates more broadly about the number of judges required to hear cases.  Why not only one judge?  Why three?  Why do we believe that there must be an odd number of judges?  Perhaps there are other reasons to call on a third or a fifth judge.  The rabbis consider the biblical instructions that are interpreted to mean that we need certain numbers of judges.  

While these explanations seem to be logical to the rabbis, I find them challenging.  For example, when considering a case requiring four judges, we are told that the first two are assigned because "they" put their hands on... the second two are chosen because it was "the Elders" who did this.  To me, this sounds like two judges, not four.  And the fifth judge is placed to ensure that there is an odd number of judges.