1. At the disco, 42 people arrived: boys and girls. Each girl danced with all the boys, except for four, and each boy danced with all the girls, except for three. How many boys were at the dance? (Folklore)
Answer: 24. Solution: Let $m$ be the number of boys and $d$ be the number of girls who came to the disco. Denote the boys by blue dots, the girls by red dots, and connect the boys and girls who did not dance with each other by segments. Let there be a total of $k$ segments. Since 4 segments come out of each red dot and 3 segments come out of each blue dot, and each segment connects a red and a blue dot, the equations $4 d=k=3 m$ are satisfied, from which $d=3 m / 4$. According to the condition, $m+d=m+3 m / 4=7 m / 4=42$, from which $m=24$.