+0  
 
0
43
2
avatar

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
avatar
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
avatar+19603 
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

 

 

laugh

heureka  Jul 2, 2018
edited by heureka  Jul 2, 2018

13 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.