1530.33 – I Have a Good Friend in Maumee

Tags:Problem Set 6Algebra IAlgebra Prep

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?


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

We are given that b=3b = 3 and a2=baa^2 = b \bigsqcup a. Therefore, her age is a3a \bigsqcup 3 and a2=3aa^2 = 3 \bigsqcup a. Now the only two-digit square number starting with 33 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!