For some integers that are not palindromes, like 91, a person can create a palindrome by repeatedly reversing the number and adding the original number to its reverse. For example, . Then , which is a palindrome, so 91 takes two steps to become a palindrome. Of all positive integers between 10 and 100, what is the sum of the non-palindrome integers that take exactly six steps to become palindromes?

Guest Jun 30, 2018

#1**0 **

I could only think of 2 numbers that would do so in 6 steps:

79 +97=176 + 671 =847 + 748=1,595 + 5,951 =7,546 + 6,457 =14,003 + 30,041 =44,044

97 + 79=176.......and so on as before.

Now, 88 is a 2-digit palindrome. If you wanted it to be more than 2 digits, it will also take 6 steps to become 5-digit palindrome of 44,044.

There are 2 numbers that I don't think you can make a palindrome out of them unless I made a mistake. And they are: 89 and 98. Try and see if you can do it.

Guest Jun 30, 2018

#2**0 **

**For some integers that are not palindromes, like 91, a person can create a palindrome by repeatedly reversing the number and adding the original number to its reverse. For example, . Then , which is a palindrome, so 91 takes two steps to become a palindrome. Of all positive integers **

**between 10 and 100, what is the sum of the non-palindrome integers that take exactly six steps to become palindromes?**

Source: https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1013&context=mathmidexppap

heureka
Jul 2, 2018