## 1530.33 – I Have a Good Friend in Maumee

I have a good friend in Maumee

Whose age’s last digit is three.

The square of the first

Is her whole age reversed,

So what must this lady’s age be?

## Solution

Assume the age of this Maumee friend is a two-digit number. Let her age be notated $a \bigsqcup b$, so that $\bigsqcup$ stands for the space between digits and her age with the digits reversed is $b \bigsqcup a$.

We are given that $b = 3$ and $a^2 = b \bigsqcup a$. Therefore, her age is $a \bigsqcup 3$ and $a^2 = 3 \bigsqcup a$. Now the only two-digit square number starting with $3$ is thirty-six. Notice that the square of its second digit is also thirty-six.

Thus the woman’s age is sixty-three. A student some years ago submitted this solution:

The woman you know in Maumee

Will soon be a new retiree

'Cause this clever fella

Just solved this here Stella:

The lady must be sixty-three!