1. A palindrome is a number where the digits read the same forwards or backwards, such as 4774 or 505 . What is the smallest palindrome that is larger than 2015 ?
Solution: Since 2015 has 4 digits, any number larger than 2015 will also have 4 digits. Given two starting digits, in order, there is a unique 4-digit palindrome that begins with those two starting digits. For starting digits 20, the palindrome is 2002 , which is less than 2015 . The next smallest will start with 21 and is 2112 . Since $2112>2015$ this is the smallest palindrome greater than 2015 .