Age of Augustus
The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?
Age
11 to 14
Challenge level
The English mathematician Augustus de Morgan, who died in $1871$, claimed that he became $x$ years old in the year $x^2$. When was he born?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Answer: 1806
Square numbers near 1871 (year of death)
40$\times$40 = 1600 too small
42$\times$42 = 1764, but if he was 42 in 1764 then by 1871 he was older than 140
43$\times$43 = 1849, 22 years before he died in 1871, which is reasonable
44$\times$44$\gt$1871 so there are no more possibilities
So he was born 43 years before 1849, in 1806