Question

If it takes 1074 digits to number the pages of a book starting with page 1. how many pages are in the book? The book has a total of pages. ​

Answer 1

• 394 pages

Explanation:

1- digit numbers:

• 1 to 9, number of digits = 9

2- digit numbers:

• 10 to 99, number of digits = 2(99 - 9) = 180

3- digit numbers:

• 100 to 999, number of digits = 3(999 - 99) = 2700

This is more than we have, but we know the number of pages is 3-digit.

Let it be x, then we have:

• 9 + 180 + 3(x - 99) = 1074
• 3(x - 99) = 1074 - 189
• 3(x - 99) = 885
• x - 99 = 885/3
• x - 99 = 295
• x = 295 + 99
• x = 394