1. In a certain table tennis singles competition, it was originally planned that each pair of players would play exactly one match, but after 3 players each played 2 matches, they withdrew from the competition. As a result, only 50 matches were played in total. The number of matches played among these 3 players is
A. 0
B. 1
C. 2
D. 3
1. B Let the number of matches among these three players be $r$, with a total of $n$ players participating.

According to the problem, we have $50=C_{n-3}^{2}+r+(6-2 r)$, which means $\frac{(n-3)(n-4)}{2}=44+r$.
Since $0 \leqslant r \leqslant 3$, upon inspection, it is found that when and only when $r=1$, $n=13$ is a positive integer.