A realistic human-shaped mannequin is made of topological-grade rubber.
All the body cavities that are accessible from outside without piercing any tissue, are faithfully reproduced, for example the digestive tract and the nostrils. Ear drums are assumed to be intact.
The interior of the dummy is coloured pink and the outside is sprayed blue.
Is it possible for the dummy to be turned inside-out to form a sphere with a few holes in such a way that only pink shows and only blue is hidden?
On
It seems pretty clear that the blue region is connected and the pink region is not. On the other hand I can imagine painting a blue band around a pink sphere and then deforming the sphere in such a way that the blue band is folded upon itself and "hidden" while the pink regions remain visible, but what you have then is not a "sphere with a few holes," you have something that looks (from the outside) like a sphere separated into two parts by a crack.
As far as I know, humans are homologous to a torus because of the digestive track. A torus cannot be bent into a sphere.