If you imagine this may be equal ! .. then find the value of : n . ( 2^2^2^2 )^2^2^2^2 = 2^2^n

Question

Find the largest possible value of positive integer N, such that N! can be expressed as the product of (N-4) consecutive positive integers?

Answer 1

(2^2^2^2 )^2^2^2^2 = 2^2^n
2^2^n=4^n -------- (1)
(2^2^2^2 )^2^2^2^2=4^4^4^4 ------------------ (2)
(1)=(2) ----> 4^4^4^4=4^n ------> **n=4^4^4=**************