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How to Calculate a Palindrome

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Written by jwvanno   

A palindrome is a number, word or sentence that reads the same forward or backwards.

A palindrome is a number, word or sentence that reads the same forward or backwards. For example: "bob" and "radar" are word palindromes. "Madam, I'm Adam"

is a short sentence palindrome. 121 or 36988963 would be a pair of number palindromes.

To build a palindrome from any number, follow these easy instructions.

Step 1 - First, write your number down on a piece of paper. We'll use 431. Now, look to see if the number you're looking at is already a palindrome. Write

the number directly below the original number, but write it backwards: 134.

Step 2 - If the two lines are the same, then you have a palindrome already, and can stop.

HOWEVER, In most cases, the two numbers will NOT be the same. For those numbers, the trick, now, is to add the two numbers together. In our example, 431 +

134 would equal 565. When we test for a palindrome, we find out that we've made one!!

Step 3 - But what happens if we use a number like 73?

It's not a palindrome by itself, and if we reverse the digits and add them together we get 110, which is also not a palindrome.

So the solution here is to reverse the digits and add them AGAIN. 110 + 011 = 121. A palindrome! (The number 0 should always be taken into account no matter

if it's on the left or right.)

Step 4 - If the new result is still not a palindrome, reverse the answer's digits, add them together and check again. Repeat as often as needed.

The number 89 is a tough one. It needs to go through the reverse and add process 24 times before it becomes a palindrome.

Step 5 - So 222 is a palindrome in itself, 431 became one on the first iteration, 73 became one on the 2nd iteration, and 89 became a palindrome after 24


Do all numbers become palindromes by reversing and adding their numbers??

Step 6 - It seems not.

196 is the first of the Lychrel Numbers, but that is a whole other topic of discussion (see: http://www.p196.org).

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