1. How many numbers are there between 99 and 1000, having at least one of their digits 7?

To solve this problem, we need to consider the numbers from 100 to 999 (since 99 is not included).

1. First, let's calculate the total number of 3-digit numbers. This is 999 - 100 + 1 = 900 numbers.

2. Now, let's calculate the number of 3-digit numbers that do not contain the digit 7. For the first digit, we have 9 choices (1-9), for the second digit, we have 9 choices (0-9, excluding 7), and for the third digit, we also have 9 choices (0-9, excluding 7). So, the total number of 3-digit numbers not containing the digit 7 is 999 = 729.

3. Subtract the number of 3-digit numbers not containing 7 from the total number of 3-digit numbers to get the number of 3-digit numbers containing at least one 7. So, 900 - 729 = 171.

Therefore, there are 171 numbers between 99 and 1000 that have at least one of their digits as 7.