If the sum of the first 20 consecutive positive odd numbers is divided by $20^2$, the result is

The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is

In a locality, the houses are numbered in the following way:

The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the other side of the road are consecutive even numbers starting from 302. The total number of houses is the same on both sides of the road.

If the difference of the sum of the house-numbers between the two sides of the road is 27, then the number of houses on each side of the road is

For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1$, $\left(\frac{p}{q}\right)^\frac{p}{q}= p^{\left(\frac{p}{q}-1\right)}$. Then,