- Sources for machlokes if מלקות requires three or twenty-three דיינים
In the Mishnah on Daf 2a, the Tanna Kamma said malkus requires a Beis Din of three judges. Rav Huna says the Tanna Kamma derives from the plural form of "ושפטום" – and they shall judge them, to require two judges, and since Beis Din cannot be an even number, we add a third judge. The other two plural terms in that passuk ("והרשיעו" and "והצדיקו") do not add another four judges, because those terms teach that עדים זוממים who cannot receive the standard "כאשר זמם" punishment incur malkus, despite the transgression being a לאו שאין בו מעשה. Rebbe Yishmael requires twenty-three judges for malkus, and Abaye explains he derives it from a gezeirah shavah ("רשע רשע") from חייבי מיתות. Rava says: מלקות במקום מיתה עומדת – malkus stands in place of the death penalty (Rashi explains that he deserves death for transgressing Hashem’s command), and is another form of a death penalty, requiring twenty-three judges. The Gemara proceeds to explain why someone receiving malkus is assessed to determine how many malkos he can endure and survive.
- "עיבור חודש" requires three judges: קידוש החודש or חישוב?
The Mishnah taught that three judges are required for "עיבור החודש" – adding a day into the month. This implies that three judges are needed to declare the previous month extended by a day, and the Gemara wonders why any declaration is necessary. If they are not מקדש the thirtieth day, it is extended automatically!? Abaye emends the Mishnah’s text to be קידוש החודש, requiring Beis Din to be מקדש every Rosh Chodesh. Rava objects that the Mishnah’s text is "עיבור", not קידוש. Therefore, Rava explains that the Mishnah means that קידוש which is on the יום עיבור – the (potentially) added day (i.e., the thirtieth day) requires three דיינים. This Tanna holds that Beis Din is only מקדש a thirtieth day as Rosh Chodesh, but not when Rosh Chodesh is the thirty-first day. Rav Nachman says the opposite, that the Tanna refers to קידוש performed by Beis Din when extending the previous month, but holds that when the thirtieth day is Rosh Chodesh, no קידוש is necessary. Finally, Rav Ashi says the Mishnah refers to "חישוב דעיבור" – calculations for determining whether an extension of the month is feasible [extending too many months causes the new moon to be sighted several days before Rosh Chodesh, appearing inconsistent with the calendar].
- Rabban Shimon ben Gamliel’s requirement of three, five, and seven דיינים for עיבור שנה
In the Mishnah, Rebbe Meir taught that עיבור שנה (adding a month to the year) requires three דיינים, but Rabban Shimon ben Gamliel says: בשלשה מתחילין – they begin with three judges, ובחמשה נושאין ונותנין – discuss it with five, וגומרין בשבעה – and finalize it with seven. A Baraisa explains that they follow the majority opinion of three judges whether to sit and deliberate about adding a month. Then five judges discuss the matter, and the majority opinion is followed to decide whether to add a month or not. If they decide it is necessary, then two more judges are added, totaling seven, to complete the process and declare a leap year. The Gemara asks what these three numbers correspond to, and two explanations are given: (1) They respond to the three, five, and seven words in the three pesukim of ברכת כהנים. (2) Three judges correspond to the three "שומרי הסף" – gatekeepers, the five correspond to the five "מרואי פני המלך" – of those ministers who saw the king’s face regularly, and the seven correspond to the seven "רואי פני המלך" – ministers who saw the king’s face.