8 cubes ($2$x$2$x$2$) crossed by a straight line

Question

There are 8 cubes forming a bigger cube whose dimension is $2$ x $2$ x $2$.
Let a straight line (or a laser) try to pierce through as many small cubes as possible.

At most how many small cubes can be pierced through by the straight line?

Answer 1

A restatement of your question: Given a line in $\Bbb R^3$, at how many points may at least one of the coordinates change sign? Certainly a max is three, so the answer to your question is four, once we find such a line. If you join $(-1,-2,-3)$ to $(1,1,1)$, that line will do it.

I think a somewhat more interesting question would deal with a $3\times3\times3$ cube.