8th Iberoamerican 1993 Problem 1 A palindrome is a positive integers which is unchanged if you reverse the order of its digits. For example, 23432. If all palindromes are written in increasing order, what possible prime values can the difference between successive palindromes take? Solution
: 2, 11. Let x be a palindrome and x' the next highest palindrome. If x  100. If x and x' have the same final digit, then their difference is divisible by 10 and hence not prime. So they must have different digits. Thus either x = d9...9d and x' = d'0...0d', where d < 9 and d' = d+1, or x' has one more digit than x and d = 9, d' = 1. In the first case x' - x = 11. In the second case x' - x = 2. So again the only prime differences are 2 and 11. 8th Ibero 1993 © John Scholes jscholes@kalva.demon.co.uk 31 July 2002