Question

If the number of three digit numbers having only two consecutive digits identical is $N,$ then the value of $(N/2{)}^{1/2}$ is

Answer 1

​Let in a three digit number first two digits are same which can be selected by $9$ ways as $0$ is excluded.
Now last digit can also be selected by $9$, because $0$ can be included here.
Hence total possible numbers in which first $2$ digits are identical is $=9\times 9=81$
Similarly if last two digits are same then total possible ways are $=81$
Hence $N=81+81=162$
$\therefore {\left[N/2\right]}^{1/2}=9$