23.39 A large cube is formed by stacking 27 small cubes. A plane is perpendicular to one of the large cube's diagonals and bisects this diagonal. The number of small cubes intersected by this plane is
(A) 16.
(B) 17.
(C) 18.
(D) 19.
(E) 20
(46th American High School Mathematics Examination, 1995)
［Solution］Obviously, the plane passing through the midpoints of the edges in the figure below is perpendicular to the diagonal of the cube and bisects it.

From the figure on the right below, we can see: there are 4 small cubes in each of the upper and lower corners of the plane that are not intersected by the plane. Thus, the number of small cubes intersected by the plane is $27-8=$ 19.
Therefore, the answer is $(D)$.