By looking at the colours one at a time, you can work out how many blocks of each colour there is in a factorial. Here are only the blue blocks in the number line from 1 to 20
The number of blue blocks in n factorial is
$\lfloor \frac{n!}{2} \rfloor + \lfloor \frac{n!}{4} \rfloor + \lfloor \frac{n!}{8} \rfloor + \ldots$
