Quandaries
and Queries 

Hello my name Lillian. I am a student in the 10th grade. My class is studying palindromes. I was wondering why 12, 21, 13, and 31 are the only doubledigit numbers whose squares are the palindromes of the squares of the palindromes of doubledigit numbers. I was wondering why it works for these numbers, and if only these numbers work this way. Thanks Lilly 

Hi Lilly, That's a really nice observation. Lets look at 13 and 31.
It's the beautiful symmetry that makes this work. A problem arises however if one of the digits is larger than 3. In this case the square of the digit is a two digit number so in the multiplication there is a carry that destroys the symmetry. By the way, don't 11, 22 and 33 meet your conditions? Chris and Penny 

