How do curved spheres intersect in 3-space?

We prove (by giving an explicit example) that the answer to this problem is “no”. We also prove a necessary and sufficient condition on M and N for existing of such intersecting spheres. This result can be restated in terms of graphs. Such restatement allows for a trivial brute-force algorithm checking the condition for any given M and N. It is an open question if a faster algorithm exists.