8.5. 10 girls and 10 boys stood in a row such that girls and boys alternate, specifically from left to right: girl-boy-girl-boy and so on. Every minute, in one (any) pair of neighbors "girl-boy," the children can swap places, provided that the girl is to the left of the boy. Can such an "exchange process" continue for more than an hour?
Answer: It cannot. Solution. Consider the numbers in order (from left to right) of all ten boys. Initially, these were all even numbers $2,4,6, \ldots, 20$. Every minute, the number of one of the boys decreases by one, and the process will continue until the numbers of the boys become $1,2,3, \ldots, 10$ (i.e., until all the boys are to the left of all the girls). The sum of the boys' numbers was initially $(2+4+\ldots+20)=2(1+2+\ldots+10)=2 \cdot 55$, and at the end, it is $(1+2+\ldots+10)=55$. Therefore, it will decrease by 55. Since this sum decreases by 1 each minute, the entire process will take 55 minutes.