23.17 The cube $C=\{(x, y, z) \mid 0 \leqslant x, y, z \leqslant 1\}$ is divided into parts by the planes $x=y$, $y=z$, $z=x$. The number of parts is
(A) 5.
(B) 6.
(C) 7.
(D) 8.
(E) 9.
(38th American High School Mathematics Examination, 1987)
［Solution］Obviously, $C$ is the unit cube in the first octant.
When it is divided by the planes $x=y, y=z$, it is split into 4 parts (see figure (1)); when further cut by the plane $z=x$, two of these parts are each divided into two (see figure (2)).
Thus, the cube is divided into 6 parts by the three planes.
Therefore, the answer is $(B)$.