I was looking into the census of the Jews in the Torah. It seems somewhat strange (and statistically unlikely) that every single tribe had a “round” number — all but one rounded to hundreds, and only one (Gad) showing a number to 50! It is especially strange since the count of First Born, which counted not from age 20 but from one month and up, was a number showing units and tens…
Furthermore, if Levi had only 300 first born (the explanation for the discrepancy between the 22,300 total of the three clans and the total 0f 22,000 quoted in the Torah), that meant one first born for every 74 males in the tribe of Levi! Even for the rest of Israel, the number of first born from age one month (22,273) means one first born for about 27 adult males aged 20 and more. What kind of family structure can explain this kind of relationship? (Even assuming multiple wives and concubines for every male, and twice the number of children that our father Jacob had, it is still hard to fathom.)
This is a great question. I have been struggling with these issues for years, and have found very little written on them in the commentaries. I’ll tell you what I know, though, and some guesses.
R’ Yaakov Kaminetsky z”l writes that the unusually small number of first born compared to the total number of males is evidence of what our Sages said, that in Egypt the Jews had tremendous numbers of children, 6 at a time. They must have had very large families.
Let me amplify your first question somewhat. Were the numbers of the tribes rounded, that is, inexact, or were there precisely the number listed? If they were rounded off, what were they rounded to? As you point out, one came out in fifties, so they could not have been rounded to hundreds. Note, though, that in the Torah portion of Pinchas, they are listed again, again they all come out to even hundreds, except for one, Reuven, which has an excess of 30! So maybe they were rounded to tens! But as you point out, it would still be stupendously statistically unlikely for all to be even hundreds (if they’re rounded by ten) except for one in Bamidbar and one in Pinchas. My rough calculation (using the Binomial Theorem) was that such a thing has 1/25,000,000,000,000,000,000 probability.
Further, the counts of the Levites all come out to multiples of a hundred, and the first born are counted down to the last one, and then we subtract! That doesn’t seem fair at all, unless the numbers of the Levites were really exact. In short, rounding does not seem to work as an explanation.
I feel that we should not look at the numbers in these portions as being simply a recording of happenstance of that time. If so, who would care about them anyhow? Rather, each tribe is an entity, and the numbers of that tribe reflect an infusion of blessing from G-d. They are a reflection of His providence. Of course, I have no idea of how G-d decides who gets what. Still, it would mean that the portions are in 100s, which is some kind of subunit within the Jewish nation (for example, there were judges of hundreds in the reading of Yisro). The fact that the numbers of all the Jews were (about) the same in Bamidbar and in Pinchos means that the Jews were in a kind of stasis in terms of their overall blessing of increase for those forty years. That the number of individual tribes changed considerably means that some kind of jockeying for position took place.
I hope you’ll pardon a perhaps fanciful illustration. Imagine someone pouring batter into cupcake pans. He fills up each little tin and goes to the next. But, when he’s done, he still has some batter left, so he makes a last little half-cupcake. In Parshas Bamidbar, Gad got that last bit; in Parshas Pinchas, it was Reuven. Just a suggestion…
It seems very significant to me that in the section about the redemption of the first born by the Levites, the word for Levites (Levi) is always plural, and the word for the first born (Bechor) is always singular. Take a look, it’s quite striking. Could be that the Levites had a subunit of 100s, whereas first born were only counted individually. If so, perhaps the subtraction was not unfair.
As you see, I have little to offer on this but my own ideas. And I have written at length, though your question was short. I hope you’ll forgive me; this is a subject which I find very fascinating, and I’m very pleased to make the acquaintance of someone else who is fascinated by it.
Best wishes,
Michoel Reach