Solution:

All $99$ positive integers below $100$ qualify. A qualifying $3$-digit number is either a repdigit ($9$ of them) or uses a leading digit $a \ge 1$ together with a second value $b \ne a$ in some of the last two positions: $2^2 - 1 = 3$ patterns, each realized in $9 \cdot 9$ ways ($9$ choices for $a,$ then $9$ for $b$), for $9 + 3 \cdot 81 = 252$ numbers.

Similarly a qualifying $4$-digit number is a repdigit ($9$) or has $b \ne a$ appearing in a nonempty subset of the last three positions: $2^3 - 1 = 7$ patterns, each in $9 \cdot 9$ ways, for $9 + 7 \cdot 81 = 576$ numbers.

The total is $99 + 252 + 576 = 927.$