MathDB

Let

S

be the set of all four digit palindromes (a palindrome is a number that reads the same forwards and backwards). The average value of

|m - n|

over all ordered pairs

(m, n)

, where

m

and

n

are (not necessarily distinct) elements of

S

, is equal to

p/q

, for relatively prime positive integers

p

and

q

. Find

p + q

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