[Kevin Ray]

One way, which may not be feasible because of the 4" constraint, is to tie a knot in a stocking, insert the egg, then knot the stocking on the other side of the egg. Now stretch the "hammock" between both ends of a rigid box. As long as the egg can't touch the sides of the box, it should withstand the fall. This worked for us in our HS physics class (shoe box, third floor). Good luck!