15. (12 points) In a plane, there are 15 red points. Some line segments are drawn between these red points. If a red point is connected by several line segments, the number of line segments is marked on this red point. It is known that red points marked with the same number are not connected to each other. What is the maximum number of line segments that can be drawn between these 15 red points? $\qquad$
【Solution】Solution: Divide 15 points into 5 groups, with each group having $1,2,3,4,5$ points,
$$
\begin{aligned}
& (1 \times 14+2 \times 13+3 \times 12+4 \times 11+5 \times 10) \div 2 \\
= & 170 \div 2 \\
= & 85 \text { (lines) }
\end{aligned}
$$

Answer: The 15 red points are connected by at most 85 line segments.
Therefore, the answer is: 85.