Such an oddity

Solution 1: There are 9 choices for each of the second and third digits. For the first digit, if the existing 2-digit number is odd, we have 4 choices (2,4,6,8) and if the existing 2-digit number is even, we have 4 choices (1,3,5,7). Thus, there are a total of $9 * 9 * 4 = 324$ such numbers.

Solution 2: Since $100_3 = 82$ and $999_3 = 729$ , hence there are $\frac{729 - 83 } { 2} + 1 = 324$ odd numbers.