Let and be five-digit palindromes (without leading zeroes) such that and there are no other five-digit palindromes strictly between and . What are all possible values of ?
Solution
Let be the digits of the palindrome . There are three cases. If , then the next palindrome greater than is , which differs by 100. If but , then the next palindrome up is , which differs from by 110. Finally, if , then the next palindrome after is , which gives a difference of 11. Thus, the possible differences are .
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