SOLUTION: If n! is NOT divisible by 1024, what is the largest possible value of n?

 
1024 is 

So the n! we are looking for must contain 2 9 or fewer times.  So we start
building up a factorial until we have the largest factorial that doesn't 
contain a 2 factor more than 9 times.

1*2*3 = 3! is the largest factorial that contains 2 as a factor only once.

1*2*3*4*5 = 5! is the largest factorial that contains 2 as a factor only 3 times.

1*2*3*4*5*6*7 = 7! is the largest factorial that contains 2 as a factor only
4 times.

1*2*3*4*5*6*7*8*9 = 9! is the largest factorial that contains 2 as a factor
only 7 times.

1*2*3*4*5*6*7*8*9*10*11 = 11! is the largest factorial that contains 2 as a
factor only 8 times.

We may not go any higher because 12! and all higher factorials will contain 2
as a factor 10 or more times. 

So the answer is that the largest possible value of n such that n! is NOT
divisible by 1024 is 11.

Edwin