De Morgan's saying: "I was x years old in the year x^2" Augustus de Morgan, when asked about his age, remarked:

I was $x$ years old in the year $x^2$.

He died in $1871$. 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 $1806$.
Is there a systematic way to answer such a question without trial and error?

The year is $x^2$ and he died in 1871. Assuming he lived less than 100 years:
$1871-100<x^2<1871$
Taking the square root of both sides
$42\le x\le44$ .
Still need trial and error, but there are only 3 candidates.
