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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?

Jun 30, 2018

#1
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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.

Jun 30, 2018
#2
+1

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