mathematics - Maximize the number of factorials in your solution to 6 5 4 3 = 1

Using the same rules as Make 6 5 4 3 = 1, but maximize the number of factorials. You may not take the factorial of 1 or 2.

This is harder than it looks. A great answer has six factorials, an amazing answer has seven factorials, and an outstanding answer has eight or more factorials.

Edit: Shoot, I should have blocked factorials of numbers bigger than twenty like I did in my program.

Answer

I'll attempt with the rule "No factorials on numbers greater than 20". Here is a solution with 7. Some formatting help is appreciated

$$\frac{6!}{(5!\div4!)!}! \div 3!!$$

Method:

I started with the observation that 6! / 5! = 6, Likewise 5!/4! = 5. 3! = 6 so 6! = 3!! I then built up from there. So 6! = (6!/(5! / 4!))!

Figured out the missing factorial:

$$\left(\frac{6!}{(5!\div4!)!}! - 3!!\right)!$$ works since 0! = 1 by definition.