Count Book Pages!
Algebra
Level
2
It takes 1629 digits to number the pages of a book. How many pages does the book have?
1440
543
189
579
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
From page #1 to page # 9, there are 9 pages
From page #10 to page # 99, there are 90 pages. However, since each page number has 2 digits, there are 180 digits from page # 10 to page # 99
From page #100 to page # 999, there are 900 pages. However, since each page number has 3 digits, there are 2700 digits from page # 100 to page # 999
Since there are 1629 digits, we know so far that number of pages is less than 900
Now, we need to find out how many digits there are for those pages greater than 99 or those pages with 3 digits
Since there are 189 digits for pages with less than 3 digits, we can subtract 189 from 1629 digits to find the number of pages with 3 digits
1629 − 189 = 1440
1440 represents the pages with 3 digits, so number of pages with 3 digits = 1440/3 = 480
Thus, total number of pages = 480 + 90 + 9 = 579 pages