Henry Ernest Dudeney/Modern Puzzles/87 - Another Street Puzzle

by : $87$

 * Another Street Puzzle
 * A long street in Brussels has all the odd numbers of the houses on one side and all the even numbers on the other.
 * $(1)$ If a man lives in an odd-numbered house and all the numbers on one side of him, added together, equal the numbers on the other side,
 * how many houses are there, and what is the number of his house?
 * $(2)$ If a man lives on the even side and all the numbers on one side of him equal those on the other side,
 * how many houses are there, and what is his number?


 * We will assume that there are more than fifty houses on each side of the street and fewer than five hundred.