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

Modern Puzzles by Henry Ernest Dudeney: $87$

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.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $87$. -- Another Street Puzzle
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $170$. Another Street Puzzle