sorted numbers

There are $9\choose2$ $=36$ sorted numbers of two digits. Now we check how many "a hundred" numbers there are: $1XX$ . We choose $2$ out of $8$ for such calculation, so we got $8 \choose 2$ $=28$ . We do the same for "two hundred", we choose $2$ out of $7$ : $7 \choose 2$ $=21$ . By now, we have $36+28+21=85$ numbers. If we count how many "three hundred" sorted numbers exist, we will find: $6\choose2$ $=15$ and we got a total of $85+15=100$ numbers so far. So, the $100^{th}$ sorted number is the biggest "three hundred" one, which is: $\boxed{389}$ .