A palindrome is a positive integer whose digits are the same when read forwards or backwards. For example, 2002 is a palindrome. What is the smallest number which can be added to 2002 to produce a larger palindrome?
(A) 11
(B) 110
(C) 108
(D) 18
(E) 1001
A palindrome is a positive integer whose digits are the same when read forwards or backwards. For example, 2002 is a palindrome. What is the smallest number which can be added to 2002 to produce a larger palindrome?
(A) 11
(B) 110
(C) 108
(D) 18
(E) 1001

## Solution

The best way to analyze this problem is by asking the question, "What is the next palindrome bigger than 2002?" Since the required palindrome should be of the form $2 a a 2$, where the middle two digits (both $a$ ) do not equal 0 , it must be the number 2112. Thus, the number that must be added to 2002 is $2112-2002=110$.

ANSwER: (B)