Question 42
A village is made up of isolated homes, connected by roads. Each of these streets is a path that connects two houses (and between two houses there is at most one path that connects them). The homes are of two types: central and peripheral. Each central house is connected to exactly three other houses; each peripheral home is connected to exactly two other homes. Knowing that the number of central houses is equal to the number of peripheral houses, and that there are 30 paths in total, how many houses are there in the whole village?