The Mathematical Mystery of a Man's Age: A 1967 Correspondent's Question

Back in 1967, a curious correspondent posed a question that intrigued mathematicians and puzzle enthusiasts alike. The query delved into the enigma of a man's age at death and birth. Let's unravel this 50-year-old mystery together and explore the mathematical reasoning behind the solution.

The Question and Initial Analysis

In 1967, a correspondent proposed the following riddle: A man’s age at death was one forty-ninth of the year of his birth. The riddle seeks to find the man’s age in 1945, given this unique condition.

Calculating the Year of Birth and Age at Death

Let's denote the man's age at death as x and the year of his birth as Y. According to the riddle, his age at death, x, is one forty-ninth of the year of his birth, Y. Thus, we can express this relationship mathematically as:

x Y / 49

Step 1: Finding the Year of Birth

The year of death has to be a multiple of 50, and it is implied that the man was alive in 1945. The only year of death that fits these criteria is 1950. This is because 1950 is the nearest multiple of 50 preceding 1945. Therefore, we can set y 1950:

x 1950 / 49

x 39

The man's age at death in 1950 was 39 years old. To find the year of birth, we subtract 39 from 1950:

Y 1950 - 39

Y 1911

Thus, the man was born in 1911 and died in 1950 at the age of 39. Therefore, his age in 1945 would be:

1945 - 1911 34

Alternative Approach

To further validate this solution, let's also consider the alternative calculations:

1. Calculation for Age 49

If the man was 49 years old at death, the year of birth would be:

Y 1945 * 49

Calculating the exact year gives:

95305 / 49 1950.010204

Since 1950 is the nearest multiple of 50, we can round to the nearest integer:

Y 5049 - 50 1950

The man was born in 1800 and died in 1850, which does not fit the criterion of being alive in 1945.

2. Calculation for Age 52

If we check for the age of 52, the year of birth would be:

Y 1945 * 52

Calculating the exact age gives:

100640 / 49 1950.000000

Again, the year of death would still be 1950, and the year of birth would be:

Y 1950 - 52

Y 1872

The man was born in 1872 and died in 1924, which fits the year of death as a multiple of 50 and being alive in 1945.

Conclusion

The only solution that fits all the given criteria is the man's age at death being 39, born in 1911, and dying in 1950. His age in 1945 would be 34, following the logic of the riddle and mathematical calculations.

In summary, the man's age in 1945, derived from the correspondence, is 34 years old. This aligns with the multiple of 50 for the year of death and the implication that he was alive in 1945.

This elegant puzzle challenges our understanding of basic arithmetic and time calculations, offering a glimpse into the fascinating world of mathematical riddles and puzzles.