Sadie wrote that her grandfather died in the year his old cow died. Now, the square root of the year he was born plus the square root of the year Sadie's daughter was born give her grandfather's age when he died. How old was he and in what year did his old and beloved cow die?
Solution
We need years in the past few centuries that are perfect squares. Here are some.
\begin{aligned}
41^2 &=& 1681 \
42^2 &=& 1764 \
43^2 &=& 1849 \
44^2 &=& 1936 \
45^2 &=& 2025
\end{aligned}
It looks as if Sadie's grandpa was born in 1849 and her daughter was born in 1936. These have square roots of 43 and 44, so her gramps lived to be 87 and died in the year , along with his cow. But also, strange to say, that's the same year Sadie's daughter was born.