32 Use $n^{3}$ unit cubes to form a cube with edge length $n$ $(n \in \mathbf{N}, n \geqslant 2)$. If a line contains a point inside a unit cube, it is said that the line passes through this unit cube. The maximum number of unit cubes that a line can pass through is
A. $3 n-2$
B. $3 n-1$
C. $2 n+1$
D. $2 n-1$
32 A. Removing the 6 faces of the large cube, the other small cubes form $3(n-1)$ planes which can have at most $3(n-1)$ intersection points with a line, dividing the line into $3(n-1)+1=3n-2$ segments, thus, the line can pass through at most $3n-2$ small cubes. On the other hand, in the large cube $ABCD-A_{1}B_{1}C_{1}D_{1}$, take point $M$ close to $A$ on edge $AB$, and take point $M_{1}$ close to $C_{1}$ on edge $C_{1}D_{1}$, then $MM_{1}$ passes through $3n-2$ small cubes.