Building a formula to pass n bits though the minimum number of circuts
Each of your X boxes reduces 4 input signals to 2.

To put it another way, each X box reduces the total number of signals by 2.

This result is the same whatever arrangement of X boxes you use: a fat tree (like the one you drew) or a long thin chain. 

If you have 2n inputs, you will always need n-1 boxes if you want only 2 outputs. 

Your “n=32” solution must therefore be wrong somehow.