When Rashi explains a complicated algebraic computation we say
that Rashi is using the spreadsheet method. Spreadsheet
Rashis have a more complicated flavor than other Rashis because
of their algebraic technical nature.
Verse Dt21-17a lays down the requirements for promogeniture:
But he shall acknowledge the firstborn son of ....,
by giving him a double portion of all that he has; ...
Rashi explains: For example if a person's estate has $1,000,000 and
he has 3 children then we do as follows: We create a fictitious son so
that the person now has 4 children, the 3 actual ones and the fictitious
one. Each son inherits one fourth of the estate $250,000. The eldest son
inherits both his share of $250,000 and the $250,000 of the fictitious
son. Consequently the first born inherits $500,000 while the other 2 actual
children inherit $250,000 each. It follows that the aggregate share of the
firstborn, $500,000, is twice the $250,000 inherited by each non firstborn.
I have augmented Rashi's explanation with the examples used by the Rambam
in Chapter 2 of Inheritances. The reader may wonder why the Rambam made
obscure so simple a law. Why not simply let the variable x denote
the unknown amount inherited by the non first born son. We see
that each real son inherits x
while the firstborn inherits 2x. Thus the firstborn inherits twice
the amount of each non firstborn. Furthermore the sum of all the inheritances
must exhaust the estate giving rise to the equation x + x + 2x = $1,000,000
which easily solves for x = $250,000 and 2x = $500,000.
The above algebraic approach is simpler for the general case.
However Rambam gives a complicated example of a 3 child family where one
of the non first born sons had an unnatural birth and is not counted for
the share of the firstborn son, but does inherit. The interested reader can look up the
Rambam's example in his great code.
We also brought the two approaches to illustrate how spreadsheet
Rashis can be approached in a variety of manners.