Quote:
Originally Posted by Kees
I get to 35 too as upperbound but I would be surprised if there were a configuration where 35 moves are actually needed

If 25 swaps are needed to make the top half all even/odd, then
at least five(?) of the boundary pieces will be involved. By doing these
first, surely we can get the cross boundary sum associated with these
pieces to be composite, reducing the 10 boundary swaps
subsequently needed.
David