Henry Ernest Dudeney/Modern Puzzles/86 - A New Street Puzzle

Modern Puzzles by Henry Ernest Dudeney: $86$

A New Street Puzzle

Brown lived in a street which contained more than twenty houses, but fewer than five hundred,

all numbered one, two, three, four, etc., throughout.

Brown discovered that all the numbers from one upwards to his own number inclusive summed to exactly half the sum of all the numbers from one up to, and including, the last house.

Now what was the number of his house?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $86$. -- A New Street Puzzle
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $169$. A New Street Puzzle