Leftovers from Yechezkel's Shabbos Table - Parshas Balak/Pinchas Challenge

I first launched this Blog after Parshas Pinchas, so I haven't had the opportunity to discuss this. We will just have to backdate this a little. This is another difficulty in Rashi on Chumash that I have not seen anybody discuss.

At the end of Parshas Balak we are faced with the "Maaseh Shittim" and Bnos Moav. At the outset Moshe instructed all of the judges of Klal Yisrael that "each should slay his people who are coupling with Baal Pe'or." Rashi explains that that means each judge was instructed to execute 2 people - "And how many judges were there? 78,600 as is written in Tractate Sanhedrin (18a)."

Note - In some Chumashim the text in Rashi reads "88,000". Many other Chumashim correct this error to the number stated in Sanhedrin - 78, 600. It remains unclear how and when this erroneous value was first scripted.

Two things about the gemara in Sanhedrin are important to note -

• The gemara in Sanhedrin is in no way associating its count to the event at Shittim.
• The gemara, by its cumulative count, implies that that each Sar Elef did not come out of each unit of 1000 and, similarly, each Sar Meah was not included in the unit of 100, and likewise for each Sar Chamishim and Sar Asara. Thereupon, Tosafos (ad loc. s.v. Nimtzau) asks the obvious question that, if this is so, the judges must be an additional population on top of the 603,550 (i.e., the true population would actually be in the area of 682,000). Tosafos suggests two answers:
  (1) The judges were above the age of 60 and are not included in the main population count. This approach is restricted to the view that those above 60 were not included in the national census. This is not universally accepted.
  (2) Perhaps, each higher officer was actually taken from within the units of 10, 50, 100, and 1000 and, as such may have held 2, 3 ,or even 4 positions. In this approach, the number 78,600 does not refer to how many individuals had judicial positions but rather, how many judicial positions there were even though there were no more than (initially) 60,355 individuals holding the positions.

It is very curious to wonder what is Rashi's approach to the gemara in Sanhedrin in light of Tosafos's question. But, the difficulty lays in the cursory understanding of Rashi in Parshas Balak where he implies that:

• The number of judges in Sanhedrin was the actual number of individual judges.
• The number (78,600) is in force at the incident at Shittim.

This poses a big difficulty as such:

Let us assume that the number of those who were judged and executed were 2 times the known number of judges - 2 x 78,600 = 157,200. Let us assume further that those executed were actually from the main population of the Jews.

We know that after the plague of 24,000 deaths the Jews were counted and arrived at a population of 601,730 (BaMidbar 26:51). Further, it seems that the 24,000 deaths occurred after the executions. This implies that immediately after the executions there were 625,730 Jews. Now, if 157, 200 Jews were indeed executed, it follows that prior to the executions there were 625,730 + 157,200 or 782,930 Jews.

However, if there was a bigger population of Jews, there must have been a bigger population of judges (about 102,562 using the formula in Sanhedrin)! If each of of those executed 2 Jews (more than 205,000) there were more Jews to start with, which means there were more judges, which means more Jews, judges, Jews, judges, Jews, etc...ad when?

So I leave it to you to answer 2 questions:

1. According to the simple understanding of Rashi, how many Jews were there to start, how many judges, and how many were executed? (Relatively easy)
2. Why has Rashi himself, and absolutely every other commentator, overlooked this issue? (I have no answer to date).

We will follow up on this, IY"H, in a few days.

Power up that abacus!

Yechezkel