6.4. A natural number is called a palindrome if it remains unchanged when its digits are written in reverse order (for example, the numbers 4, 55, 626 are palindromes, while 20, 201, 2016 are not). Represent the number 2016 as a product of two palindromes (find all options and explain why there are no others).
Answer: 8.252. Solution: The number 2016 is not divisible by 11. Therefore, none of the palindromes are two-digit (they all are divisible by 11). This means one of the palindromes is a single-digit (if both factors have at least 3 digits, the product is no less than $100 \cdot 100 > 2016$). The number 2016 has only the following single-digit divisors: 1, 2, 3, 4, 6, 7, 8, and 9. They correspond to the factorizations $1 \cdot 2016, 2 \cdot 1008, 3 \cdot 672, 4 \cdot 504, 6 \cdot 336, 7 \cdot 288, 8 \cdot 252, 9 \cdot 224$. Only one fits.

Criterion: 2 points for the correct answer without justification. In a trial-and-error solution, each missed option results in a 2-point penalty.