Question

A man born in the first half of the nineteenth century was x years old in the year x^2. Find the year in which he was born.

Answer 1

hat means he was born between 1800 and 1850.

The square root of 1850 is 43.01162634, so the last year that was a square

before 1850 was 432 or 1849. So he was 43 years old in 1849.

So he must have been born 43 years earier in 1849-43 = 1806.

[Incidentally anybody who was or will be 35 years old in some part of 2015

will be 45 in the year