Making Sense of the Census

Everyone knows that the total number of adult men in the midbar was 600,000. In fact, there are a few specific halachos that are learned from that number. An example would be, the number of people needed [according to most Rishonim] in an area to qualify as a biblical reshus harabbim (See Rashi Eruvin 6b).

However, the results of the census taken in the midbar and recorded in the Torah, indicates that there were more than 600,000 people. The exact number given is 603,550. Why the discrepancy? Why do we not require 603,550 people to create a rishus harabbim?

I heard the following brilliant explanation from Rabbi Yisroel Reissman in his motzai shabbos nach shiur:

In parshas ki setzei the posuk relates regarding Amalek:

אֲשֶׁר קָרְךָ בַּדֶּרֶךְ, וַיְזַנֵּב בְּךָ כָּל-הַנֶּחֱשָׁלִים אַחֲרֶיךָ
how he met thee by the way, and smote the hindmost of thee, all that were enfeebled in thy rear

Who were these "enfeebled" people that Amalek smote? Rashi quotes the medrash that these were the members of the erev rav who were outside the protective cover of the ananey hakavod.

Now if it can somehow be demonstrated that these people numbered 3,550, we would understand why the gemorah refers to 600,000. That would be the total number of people that were actually inside the machaneh.

In this weeks parsha, parshas vayakhel, we read how most of the silver that was collected through the machatzis hashekel, the 1/2 shekel per person donation, was utilized for the construction of the adonim, the bases for the kerashim. There was however a small amount of silver that was left over after all the adonim were completed. This silver was used to make the hooks that held the curtains that surrounded the perimeter of the mishkan.

How did Moshe determine who's donations would go for the adonim and who's donations would be used for the hooks? The hooks were on the outside of the mishkan in an area where there was no kedusha (min ha-klayos v'lachutz). It would be a safe assumption that Moshe would use the donations of the erev rav for these hooks. (The donation of those that were outside ot the machaneh would be used on the outside of the mishkan.)

How much silver was left over and used to fabricate the hooks? The pasuk says:

וְאֶת-הָאֶלֶף וּשְׁבַע הַמֵּאוֹת, וַחֲמִשָּׁה וְשִׁבְעִים, עָשָׂה וָוִים, לָעַמּוּדִים
One thousand, seven hundred and seventy five shekalom worth of silver.

If our assumption is correct, that the erev rav were the ones that donated the silver for the hooks, we can now determine the exact census of the members of the erev rav. Bearing in mind that each person donated a 1/2 shekel, it would follow that this silver was received from 3,550 people. 3,550 individuals. 3,550 people who were outside of the machaneh. Which leaves us with exactly 600,000 people inside of the machaneh.

גַּל-עֵינַי וְאַבִּיטָה נִפְלָאוֹת, מִתּוֹרָתֶךָ.