jmc

The only three digit numbers which are ruled out are numbers of the form $ABA$, where A and B are different digits. There are 9 ways to choose A, since it can't be 0, and once A has been chosen there are 9 ways to choose B. Since there are $9\cdot 10\cdot 10=900$ total three digit numbers, and $9\cdot 9=81$ numbers which aren't valid, there are $900-81=\boxed{819}$ valid numbers.