30. Preparing for the club lesson, the children found such 2 natural consecutive numbers, the smallest of the possible ones, that the sum of the digits of each of them is divisible by 17. What numbers did the children find?
30. The smallest number, different from 0, divisible by 17 is 17, the next one is 34. The sum of the digits of one of the desired numbers should equal 17, and the other should equal 34. To make the number as small as possible, its digits should be as large as possible. For example, if we take 7999, then $9 \cdot 3+7=34$, but the next number 8000 has a digit sum of 8. Consider the number 8899, which is greater than 7999. The sum of its digits is $8 \cdot 2+9 \cdot 2=34$. The next number, 8900, has a digit sum of $8+9=17$, which satisfies the condition.