Question: A correspondent, in 1930, proposed the following question. The reader may think, at first sight, that there is insufficient data for an answer, but he will be wrong:
A man's age at death was one twenty-ninth of the year of his birth. How old was he in the year 1900?
Answer: The man was born in 1856 and died in 1920, aged 64 years. Let x = age at death. Then 29x = date of birth. The date of birth + age = date of death, so that 29x + x = 30x, or date of death. Now, from the question he was clearly alive in 1900, and dead by 1930. So death occurred during or between those dates, and as the date is 30x, it is divisible by 30. The date can only be 1920,
which, divided by 30, gives 64. So in 1900 he was 44 years of age.
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