27・11 In a space (three-dimensional) rectangular coordinate system, the number of lines passing through four different points of the form $(i, j, k)$ is $(i, j, k$ are positive integers not exceeding 4. $)$
(A) 60.
(B) 64.
(C) 72.
(D) 76.
(E) 100.
(32nd American High School Mathematics Examination, 1981)
［Solution］Consider the space (three-dimensional) Cartesian coordinate system containing all $(i, j, k)$ grid points, where $1 \leqslant i, j, k \leqslant 4$.

Then, its 4 main diagonals all pass through four different points that satisfy the condition; there are also 24 diagonals parallel to the coordinate planes, which also have this property;

In addition, there are 48 lines parallel to one of the axes, which also pass through four such points (there are 16 such lines in each axial direction).

Therefore, there are a total of $4+24+48=76$ lines passing through four different points that satisfy the condition.
Hence, the answer is $(D)$.