The solution to the problem:
1. Choose the first digit in $9$ ways and place it at the first place.
2. Choose the second digit in $9$ ways
3. Now, fill in the last three gaps: $2^3 -1$ because we don't want numbers composed of only one digit, so the answer is $9\cdot9\cdot(2^3-1)$
Now, here comes my question: the subtraction in the parentheses prevents numbers like $1111, 2222, 3333 ... 9999$. Thus, in fact, it removes 9 numbers from our set. Thus, my question is: What would $9\cdot9\cdot2^3-9$ mean? What numbers would we be counting more than once?