when is insertion sort faster than merge sort?

Question

For a homework problem, I was told that insertion sort runs at 8n^2 and that merge sort runs at 64(n(lg n)). As part of the solution I was given, it said that insertion sort was

Answer 1

It came from this (algebraic) line of reasoning

steps_in_insertion_sort <= steps_in_merge_sort
8n^2 <= 64n lg n
n^2 <= 8n lg n
n <= 8 lg n

Then 43 works by trial and error, or by solving for the zero of the equation n - 8 lg n = 0.

For hacking by trial and error, note:

$ python
>>> 8 * log(43)/log(2)
43.41011803761678

Because "lg" means log-base-two.

(Aside: calculations like this do not really translate to any real-world indication that one algorithm will beat another. Seriously, exactly 43?)