7.16 Suppose in space there are given $n$ segments, where no 3 of them are parallel to the same plane, and the line connecting the midpoints of any two segments is the common perpendicular of these two segments. Find the maximum possible value of the number of segments $n$.

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[Solution] The maximum possible value of $n$ is 2.
If there are 3 segments satisfying the requirements of the problem, let the midpoints of the three be $M_{1}, M_{2}, M_{3}$, and let the plane determined by $M_{1}, M_{2}, M_{3}$ be $\sum$. At this time, each of the 3 segments is perpendicular to two of the three lines $M_{1} M_{2}, M_{2} M_{3}, M_{3} M_{1}$, and thus perpendicular to the plane $\sum$. This leads to the 3 segments being parallel to the same plane, which is a contradiction. This shows that the number of segments $n$ is at most 2. And $n=2$ is certainly achievable, hence the maximum value of $n$ is 2.