4 Spheres all touching each other?? If there are 4 spheres all touching each other and 3 of them have diameters 4, 6 and 12 what is the diameter of the fourth one?
 I imagine it like 3 balls on a flat table touching each other and then we are supposed to put another one on top of them but in my imagination the top sphere could be any size basically right?

Just complementing the answer just posted. If the new sphere is sufficiently small, it will fit in the hole in the middle, so we have a lower bound for the size of the new sphere.
Similarly, if the new sphere is large enough, it might also make one of the previous spheres' size to be "sufficiently small", thus there might be an upper bound.
