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 double-digit numbers whose squares are the palindromes of the squares of the palindromes of double-digit 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.
1 3 3 1 1 3 3 1 --------- -------- -------- -------- -------- -------- 3 9 3 1 1 3 9 3 --------- -------- -------- -------- -------- -------- 1 6 9 9 6 1
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