two issues here:

first:

The number of 2 digit pages is 90, not 45.

If there were only 45 2 digit numbers, the pages would go

1,2,3,4,5,6,7,8,9,10,.......58,100

which is not correct as there would be pages missing between 58 and 100.

second:

The number of digits in the 3 digit pages is

195 - (number of digits in 1 digit pages) - (number of digits in 2 digit pages)

=195 - 9 - 90*2

= 6