Matematické Fórum

Skrytý text:
Each of the parts is uniquely identified by a tripple of halfspaces w.r.t. these planes. Since halfspaces x>y, y>z, z>x have no intersection and so do thir complements, there can be at most 6 pieces. And since all six other posibilities contain at least one point (we can rearange coordinates of (0.2,0.4,0.7) to fit exactly into one of these intersections; for each of 6 permutations of its coordinates it will b different intersection), the answer is 6.