Question

The pages of a 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

The digit 3 occurs between 30 & 39: 11 times.
                                   from 1 to 29 - 3 times
                                   from 40 to 99  - 6 times.

Thus the digit 3 occurs 20 times in 100.

So up to 299, the digit 3 occurs : 3 * 20 = 60 times

3 occurs 11 times each from 300 to 309, 
         from 310 to 319 and from 320 to 329.

So Up to 329 , 3 occurs 93 times

Let us enumerate the next few numbers:  330,331,332,333,

So up to page 332, the occurrence of 3 is 99 times.

Last page : 332