Henry Ernest Dudeney/Puzzles and Curious Problems/52 - In the Year 1900/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $52$

A man's age at death was one-twenty-ninth of the year of his birth.

How old was he in the year $1900$?

$44$.

This puzzle was presented in $1932$.

Years immediately before then which are divisible by $29$ are:

$1827 = 63 \times 29$

$1856 = 64 \times 29$

$1885 = 65 \times 29$

$1914 = 66 \times 29$

The years of death for each of these can then be calculated as:

$1827 + 63 = 1890$

which is too early, as it is implied he was still alive in $1900$.

$1856 + 64 = 1920$

which produces the valid solution that he was $44$ in $1900$.

$1885 + 65 = 1950$

which, in $1932$, is still in the future, so he has not died.

$\blacksquare$