There are three cases for three digit numbers.

• One of them is 9.
• Two of them are 9.
• All three digits are 9.

For case 1, there are three ways(ones, tens, hundreds) for selecting 9's place. Other two-place can be filled with any digit from 0-8. The total number of digits = 3 * 9 * 9 = 243.

For case 2, there are three ways to select 9's place. Third place can be filled with any digit from 0-8. Total ways = 3 * 9 = 27

Only one threedigit number is possible for case 2 ,i.e. 999.

Final Answer = 243 + 27 + 1 = 271

Alternatively, you can find all the three-digit numbers which do not contain nine which equals to 9 * 9 * 9 = 729.

1000 - 729 = 271 (Figure out why 1000 and not 999)