1. A palindrome is a number that reads the same from left to right and from right to left. For example, the numbers 353 and $4884-$ are palindromes. It is known that a three-digit number $x$ is a palindrome. To it, 32 was added and a four-digit number was obtained, which is also a palindrome. Find $x$.
# Answer: 969.

Solution. Since $x+32$ is a four-digit number, the inequality $x+32 \geqslant 1000$ holds, from which $x \geqslant 968$. From the fact that $x$ is a three-digit palindrome, we get that this number starts and ends with the digit 9, and its middle digit is not less than 6. By checking the four possible options, we find the only answer.

Evaluation. If the answer is found but its uniqueness is not proven, 6 points. For a complete solution, 12 points.