My workplace has a policy to provide standing desks upon request, but no policy to provide chairs of matching height. (I work for the government...) We can buy our own, or build our own. However they added a stipulation that the chairs must be bought or built with five or more wheels.
Since five is an awkward symmetry to measure and to sit in, I'd probably build my chair with six wheels. Or perhaps eight because I can start with a square and lop off the corners to make an octagon base. Or maybe make the base a perfect circle and line the bottom with innumerable tiny wheels?
This set me to wondering: is there any situation in which a chair with N+1 wheels is strictly less stable than a chair with N wheels?
To make the question interesting and rule out trivial answers, assume that the wheels are more-or-less at the chair's perimeter and more-or-less evenly distributed. Assume the floor is flat.