In Bokanovsky's Process, the embryos double when they start budding. Although the DHC says that each embryo can produce between "8 and 96" babies. How do you get 96 by doubling?
I don’t think the existing answer is correct, for two reasons:
The text it cites about “twos and threes” is not referring to Bokanovsky’s Process, but is actually contrasting the process to the old natural way in which an egg might divide into two or three.
Even were the “twos and threes” referring to Bokanovsky’s Process, the answer relies on there being five divisions. However Bokanovsky’s Process is only viable up to three divisions (as mentioned in the quote below).
How then can the figure of 96 embryos be reached? I believe this becomes clear if we look at the full description of the dividing process:
He pointed. On a very slowly moving band a rack-full of test tubes was entering a large metal box, another rack-full was emerging. Machinery, faintly purred. It took eight minutes for the tubes to go through, he told them. Eight minutes of hard X-rays being about as much as an egg can stand. A few died; most put out four buds; some eight; all were returned to the incubators, where the buds began to develop; then, after two days, were suddenly chilled, chilled, and checked. Two, four, eight, the buds in their turn budded; and having, budded were dosed, almost to death with alcohol; consequently burgeoned again and and having budded — bud out of bud out of bud — were thereafter — further arrest being generally fatal — left to develop in peace. By which time the original egg was in a fair way to becoming anything from eight to ninety-six embryos — a prodigious improvement, you will agree, on nature. Identical twins — but not in piddling twos and threes as in the old viviparous days when an egg with sometimes accidentally divide; actually by dozens, by scores at a time.
From this paragraph it is clear that the divisions are variable, where each division can result in two, four, or eight divided parts. Over the course of three divisions, there are, then, many possible permutations. Most of the permutations won’t result in 96 embryos, but some of them will.
For example, if an egg divides into eight parts on the first round, then each of those eight parts can be divided into two, four, or eight parts. Let’s say of those eight, five of them divide into four parts, and three of them divide into two parts, giving us twenty-six parts. In the final round of division, if nineteen of them divide into four parts, six divide into two parts, and one divides into eight parts, we have (19X4)+(6X2)+(1X8)=96. Notice that in my example I have most of the parts dividing by four — it is clearly specified in the aforecited text that most of the divisions are into four parts.
Of course, there are other ways to reach 96 parts as well. The point is that not all eggs will end up with 96 embroyos; 96 is merely the most that can occur. This is explicitly stated a few paragraphs later;
Ninety-six seemed to be the limit; seventy-two a good average.
(Note that this is apparently a biological limit rather than a mathematical limit, as mathematically it should be possible to get up to 512 if each one divides into eight parts.)