The Palindrome Numbers

Palindromes are words or numbers that read the same forwards and backwards eg. EYE, RACECAR, 1221.

The Sator Square

A Roman graffiti artist, in the first century AD, made a square grid of some mysterious words in the city of Pompeii. This is what it looked like

                                            
                                            SATOR
                                            AREPO
                                            TENET
                                            OPERA
                                            ROTAS

The words can be read horizontally or vertically and if all the words are put together they form a sentence which reads the same forwards and backwards :

                   SATOR AREPO TENET OPERA ROTAS

This when translated reads " The sower Arepo holds the wheels with effort". There are many more interpretations to this. 

But enough of this historical trivia ! The point is that Palindromes are so much fun. Although,  most of us have been aware of the palindromes in words, very few know that some of the numbers can be palindromic as well. There are many ways in which  numbers can be toyed around with to get palindromes. Quickly grab your calculator and punch the following :

                                              3 x 7 x 11 x 13 x 37

So what did you get? Isn't it amazing! You can make patterns in numbers appear from nowhere. Are you able to figure out anything more intriguing about this palindromic answer you got ? Confused? Let me come to your rescue.

The answer to the above operation is 111,111.

Interestingly, the number 11 makes some striking patterns.

1  x 1 =                                               1

11  x 11 =                                         1 2 1

111  x 111 =                                   1 2 3 2 1

1111  x 1111 =                             1 2 3 4 3 2 1

11111  x 11111 =                       1 2 3 4 5 4 3 2 1

This will keep on continuing till you reach number 111111111. Do you want to have more fun with this palindromic pattern? If you square the above number, you will get 12,345,678,987,654,321 which is of course a Palindrome. Only problem being, you will have to do the above calculation manually as your regular faithful calculator will not display numbers beyond 12 digits !

As mentioned earlier, there are many palindromic number patterns out there, which would be constantly discussed here.  Do you know of any interesting number palindromes you would like to share here?