14. Find how many three digit numbers, lying between 100 and 999 inclusive, have two and only two consecutive digits identical.
14. Answer: 162 .
There are two possible formats for three digit numbers to have two and only two consecutive digits identical:
(i) $\overline{a a c}$ where $a \neq 0$ and $c \neq a$, or
(ii) $\overline{a b b}$ where $a \neq 0$ and $a \neq b$.
Thus the number of such integers is
$$
9 \times 9+9 \times 9=162 \text {. }
$$