This Tuesday is a special day. It’s the only truly palindromic day in 2022. The date is 22-02 2022, a number that reads the same forwards and backwards. The day has been nicknamed ‘Twosday’.
We know more about word palindromes than their numeric equivalent. Examples are words like DAD, DEED, HANNAH and of course ABBA. There are also palindromic sentences like:
“Able was I ere I saw Elba”
And the more complex:
“Was it a car or a cat I saw?”
Making palindromic numbers
Here is a nifty little method for coming up with palindromic numbers. It is slightly addictive and works most times… a nice party trick.
Start with something simple – a 2 digit number.
Let’s say you chose 18 – write it down. Then invert the number and write it below.
Add the numbers together and you get 99, which is a palindromic number.
Now try something bigger
Inverting gives 74
When you add together you get 121 which is indeed palindromic.
If it doesn’t work straight away you may have to keep repeating the process…
Invert to give 96 and add the numbers together to get 165. This , of course is not palindromic so we repeat the process. Invert 165 to give 561 and add… keep going. You can see the process below.
|165 (Add the two numbers above. This is not palindromic and so invert and add again – see below)|
|726 (Still not palindromic and so repeat the process)|
|1353 (And again)|
|4884 (And now we have a palindrome)|
Why not try some more yourself? Maybe don’t try 196… or try it and see how far you get.
Squares, cubes and prime numbers
There are some palindromic square numbers, like 121 (which is 11 squared) and 10201 (which is 101 squared.
And some cubes are 343 (7 cubed) and 1331 (11 cubed).
And then we come to the prime numbers which are palindrome. (A prime number only divides by 1 and the number itself.) A couple of prime palindromes are 151 and 383. You can find more here.
The history of palindromes
The word actually comes from the Greek ‘palindromos’ which means to run back again. Palindromic sentences go a few thousand years back. There is even a story about Greek poet called Sotades, who lived in Egypt in about 276BC during the reign of Ptolemy II. Sotades wrote a palindrome about the king. This was not appreciated and had rather unfortunate consequences. Sadly Sotades was sealed in a box and cast out to sea!
If you’re not enjoying this then you may have an irrational fear of palindromes, known unofficially as aibohphobia. (Read carefully)