## 53. Math Puzzle 10/69

At the beginning of a group meeting, the Pioneers greet each other with handshakes. A total of 66 handshakes are exchanged.

How many friends attended the meeting?
Each of the $x$ participants shook $x-1$ hands. It is important to note that two friends always shook hands simultaneously. Therefore, the equation is:

$$
\frac{x(x-1)}{2}=66 \rightarrow x^{2}-x-132=0 \rightarrow x_{1}=12, x_{2}=-11
$$

The negative solution does not make sense in this context. Therefore, 12 friends attended the meeting.