Question

the pages of the book are numbered consecutively;1,2,3,4, and so on. no pages are missing. if in the page numbers the digit 3 occurs exactly 99 times, what is the number of the last page?

Answer 1

3 occurs 3 times from 1 - 29
3 occurs 11 times from 30 - 39
3 occurs 6 times from 40 - 100
So. 3 occurs 20 times up to 100 pages
3 occurs 60 times till page 299.
3 occurs 11 times from 300 - 309.
3 occurs 11 times from 310 - 319
3 occurs 11 times from 320 - 329
3 occurs 6 times from 330 - 332
So, 3 occurs totally 99 times till page 332.
Therefore, the last page no. is 332.