Generate all permutations of 1 to n with i stacks
What is the minimum value of $i$ which can generate all permutations of 1 to $n$ at the output?
  The options are: 1) 1 $\;$ 2) 2 $\;$ 3) $n-1$ $\;$ 4) $n$


None of the given options are correct.


All permutations of 1 to 7 can be generated by 3 stacks. 
The permutation 7132465 cannot be generated by 2 stacks.


The above facts can be verified by an exhaustive search by a program easily. So the minimum value of $i$ which can generate all permutations of 1 to 7 is 3. Note that $3\not=2$ and $3\not=7-1$.

Let $s_i$ be the minimum value of $i$ which can generate all permutations of 1 to $n$. Then
$s_1=0$, $s_2=s_3=1$, $s_4=s_5=s_6=2$, $s_7=s_8=3$. 

It is not clear to me what are the value of $s_i$ for $i\ge 9$.