Question

A person writing a book numbered the pages consecutively starting with 1 and had written 4553 digits. how many pages had she numbered?

Answer 1

single digits 1-9 or 9 --- 9 digits used
double digits 10-99 or 90
using 2 digits each gives us --- 180 digits used for doubles
triple digits 100 - 999 -- 900
using 3 digits each , 900x3 = 2700 used for triples

number of digits used for 4 digits numbers
= 4553 - 9 - 180 - 2700 = 1664
number of pages using 4 digits = 1664/4 = 416

she had numbered 1415 pages

(it is not 1416,
since 1000 is the first of the 4 digits
1001 is the 2nd of the 4 digits
.
.
1415 is 416th of the 4 digits numbers)