Problem 1. A group of schoolchildren decided to buy pizza. Each pizza is cut into 12 pieces. They calculated that if each boy eats 7 pieces and each girl eats 2 pieces, then three pizzas would not be enough. If they buy four pizzas, then each boy can have 8 pieces and each girl can have 4 pieces, and there will still be some left over. How many boys and how many girls are in this group?
Answer: 1 girl and 5 boys.

Solution: Let the number of boys be $m$, and the number of girls be $d$. Notice that $7 m+2 d > 36, 8 m+4 d \geq 14$, from which we get $m \geq 5$. But then from the inequality $4 m+2 d \leq 22$ we get that $d \leq 1$, so either $d=0$ or $d=1$. If $d=0$, then $7 m > 36, m > 5$, and $8 m \leq 44, m \leq 5$, a contradiction. If $d=1$, then $7 m > 34, m \geq 5$, and $8 m \leq 40, m \leq 5$, from which $m=5$.