2. [5 points] Several pairwise distinct natural numbers are written on the board. If the smallest number is multiplied by 35, the sum of the numbers on the board will become 592. If the largest number is multiplied by 16, the sum of the numbers on the board will also become 592. What numbers could have been written on the board?
# Answer: $15,16,17,34$ or $15,33,34$.

Solution. Let there be $n$ numbers $x_{1}35 x_{1} \geqslant$ $35 \cdot(15 \cdot 2)>592$, which is impossible. Therefore, $k=1$, from which $x_{1}=15, x_{n}=34$.

Then $35 x_{1}+x_{n}=32 \cdot 15+34=559$, and the sum of the remaining numbers is $592-559=33$, and the remaining numbers are greater than 15 and less than 34. If there is only one number, it is equal to 33. If there are two, the different natural numbers with a sum of 33 are only 17 and 16. There cannot be more than two numbers, as their sum would exceed $15 \cdot 3=45$.