1. A natural number is called a palindrome if it remains unchanged when its digits are written in reverse order (for example, 626 is a palindrome, while 2015 is not). Represent the number 2015 as the sum of two palindromes.
Answer: $2015=1551+464$

Comment. To find the solution, one could reason as follows:

Since 2002 does not work, the larger addend must be of the form $\overline{1 \text { AА1 }}$. Then the second addend must end in 4, as it equals 2015 - $\overline{1 \text { AА1 }}$, i.e., it has the form $\overline{4 \mathrm{~B} 4}$. Thus, $2015-\overline{1 \mathrm{AA} 1}=\overline{4 \mathrm{B4} 4}$. We get

$$
2015-1001-404=\overline{\mathrm{AA} 0}+\overline{\mathrm{B} 0}
$$

i.e., $61=\overline{A A}+B$, from which $\overline{A A}=55, B=6$.

Grading criteria.

## - Correct example - 7 points.

It is not necessary to provide a proof that others do not work or the reasoning used to find the example.

- Incorrect example - 0 points.