You have given a strip which is divided into n+1 identical parts by n folds on the strip. Now find the no. Of ways in which you can fold the whole strip into a single identical part..!
With the restriction imposed by $n$ folds producing $n+1$ identical parts (folding the strip in half and in half again results in $4$ identical parts but there are actually $3$ folds in the strip's single thickness), then the number of ways to fold the strip into identical parts is $2^n$. Conceptually, each fold can go in one of two directions so the $2$ possibilities of the first fold is followed by $2$ possibilities for the next fold etc. Each resulting configuration of folds has a similar configuration with surface A flipped with surface B. There are practical limitations of actually doing this for some folding configurations as n gets large.