Pages in a book - need to verify my solution

Hi All,

I have solved this problem below. But the required answer and my answer don't match. Please help me find the mistake in my solution.

The pages of a book are numbered as 1, 2, 3, .... It is found that 195 digits are used.

(a) How many pages are numbered with a single-digit number?

(b) How many pages are numbered with a two-digit number?

(c) How many pages are there altogether?

(a) I got single-digit numbers = 9

(b) I got, two-digit numbers = 99 - 9 = 90

(c) This is the part I need verified.

$\displaystyle

\begin{tabular}{ l l }

\textnormal{No. of 1 digit pages} &= 9 \\

\textnormal{No. of 2 digit pages} &= \begin{math}\frac{90}{2}\end{math} = 45 \\

\\

\textnormal{No. of 3 digit numbers used} &= 195 - 99 = 96 \\

\textnormal{No. of 3 digit pages} &= \begin{math}\frac{96}{3}\end{math} = 32 \\

\\

\textnormal{Total pages} &= 9 + 45 + 32 = 86 \\

\end{tabular}

$

The required answer is 101, I am not sure how to get there. Can you help identify my mistake. Thanks for your help.