Brainteaser

1872

Thanks, but any chance of showing how you got that answer or is too long winded?

You might want to check the answer before offering thanks.

The 19th century runs from 1801 to 1900. From the second part, you can set up two quadratic equations:

2c^2 - 2c - 1801 = 0 implies c > 30.51
2c^2 - 2c - 1900 = 0 implies c < 31.33

If 2c (his age) is an integer, then c must be 31.
2*31^2 - 2*31 = 1860 (year of birth)

No need to solve the quartic equation since this provided a single solution in the 19th century.