## Task B-2.2.

A natural number is said to be a palindrome if it reads the same from left to right and from right to left in decimal notation. We can order palindromes by size. Determine the 2010th palindrome in this order.
## Solution.

There are 9 one-digit $(1,2,3, \ldots, 9)$,

9 two-digit $(11,22,33, \ldots, 99)$,

90 three-digit (numbers of the form $x y x$),

90 four-digit (numbers of the form xyyx),

900 five-digit $(x y z y x)$,

900 six-digit $(x y z z y x)$ palindromes.

This totals 1998 palindromes.

Let's count the 7-digit ones. There are 10 numbers of the form 100x001. Therefore, 1010101 is the 2009th palindrome, and 2010th is 1011101.