Question 945583
The digit 1 sometimes appears more than once on the same page number,
so it appears a lot.
It appears at {{{100}}} times as the first digit in pages 100 to 199.
It appears as the last digit {{{50}}} times
(on page 1, and in other page numbers preceded by 1, 2, 3, ... 49).
It appears as the tens digit in {{{10}}} 2-digit numbers (10, 11, ...19),
and also appears as the tens digit in many 3-digit page numbers,
{{{10}}} times preceded by each of the {{{4}}} digits 1, 2, 3,and 4.
So, the total count is
{{{100+50+10+4*10=100+50+50=highlight(200)}}} appearances of the digit 1.
 
NOTE:
That does not mean that there are 200 page numbers where the number 1 appears.
That would be a different question.
In that case, I would rename the page numbers as the 3-digit numbers
001, 002, 003, .... 498, 499, 000.
(I am using 001 for 1, 002 for 2, and so on up to 099 for 99, and I use 000 for 500).
Those are 500 3-digit ordered arrangements,
with 5 choices for the first digit,
and 10 choices for each of the other two digits.
There is a total of {{{5*10*10=500}}} such arrangements.
How many contain the digit 1 at least once?
How many do  not contain y=the digit 1 at all?
If we wanted to exclude the digit 1,
we could only use {{{4*9*9=324}}} of the {{{500}}} arrangements.
so {{{500-324=176}}} pages contain the digit 1 at least once.