Factorial Base 4

Let \(N\) be the number of digits of \(\large {\dfrac{(1000_4)!}{(332_4)!}}\) in base 4. Find \(N\).

Notations:

  • \(!\) represents the factorial notation.

  • \(a_b\) means \(a\) base \(b\). The numbers in the problem above are in base 4.


This problem is from the Who Wants to Be A Mathematician competition.
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