Answer to Problem of the Week for 08/28/2000

Answer to August 28, 2000 Problem

de Morgan's Age Problem

Augustus de Morgan, when asked about his age, remarked, "I was x years old in the year x^2." When was he born if he died in 1871?
Solution to Problem: Answer is 1806 Examining possible squares, we find 41^2 = 1681 42^2 = 1764 43^2 = 1849 44^2 = 1936 Clearly, the only one which makes sense in this problem would be 43^2 = 1849. So de Morgan was 43 in 1849. Therefore, he was born in 1806.

Augustus de Morgan, when asked about his age, remarked, "I was x years old in the year x^2."

When was he born if he died in 1871?

Solution to Problem:

Answer is 1806

Examining possible squares, we find
41^2 = 1681
42^2 = 1764
43^2 = 1849
44^2 = 1936

Clearly, the only one which makes sense in this problem would be 43^2 = 1849. So de Morgan was 43 in 1849. Therefore, he was born in 1806.