There's a version of this with "4"s that I have done through 20. I have used factorials and square roots but nothing more. I felt dirty. BUT I did not use "44"

There's a version of this with "4"s that I have done through 20. I have used factorials and square roots but nothing more. I felt dirty. BUT I did not use "44", which I did see in some solutions. That seemed out of bounds to me!