7.2. Find the sum of all three-digit natural numbers that do not contain the digits 0 or 9 in their representation.
Answer: 255 744. Solution. We will add the numbers in a column. Each last digit (for example, two) appears in the units place as many times as there are three-digit numbers of the specified form with this last digit (in our case -- these are numbers of the form $\overline{x y 2}$, where $x, y$ are any digits from 1 to 8 inclusive.). This means that the digit two, like any other digit from 1 to 8, will appear in the units place $8 \cdot 8 = 64$ times. Thus, the sum of the digits in the units place is $64 \cdot (1+2+\ldots+8)=2304$. Similarly, in the tens and hundreds places, we get the same sum of 2304. In the end, the sum of all the numbers is

$$
2304 \cdot 100 + 2304 \cdot 10 + 2304 = 2304 \cdot 111 = 255744
$$