I was working on a problem where you have to find the biggest palindrome that you can as long as it is between 10-99. After i found that 89 was a good palindrome I let other people actually find out how long it would go on[ It turned out be 24]. I started think about if the number was prime of if it’s square root would have any effect on it. Then while randomly thinking i found the if you took a number like 19 added it with its palindrome to get   110 then I take 19 or 91 and add 9 to 1 or 1 to 9 to get 10. Then i take 110 and divide it by 1o to get 11. You will get 11 for every number under 100 i have not had much success from numbers over 100.