17. Students were given the task to write several different three-digit numbers that do not contain the digit 7 in their notation. How many such numbers can be written in total?
17. First, let's calculate the number of three-digit numbers in which there is at least one digit 7. Firstly, we notice that from 700 to 800, there are 100 such numbers; secondly, within each other hundred, there are 19 such numbers. (For example, from 100 to 200, the numbers with the tens digit 7 will be 10. These are the numbers 170, $171, \ldots, 179$. The numbers with the units digit 7 are also 10. These are the numbers 107, $117, \ldots$, 197. In total, $10+10=20$. But the number 177 is counted twice, so $20-1=19$.) The total number of three-digit numbers with the digit 7 will be $19 \cdot 8+100=252$. Considering that there are 900 three-digit numbers in total, the number of three-digit numbers in which there is no digit 7 at all is $900-252=648$.