# 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?

1
by evanex

2015-04-08T13:28:00+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Page numbers with the digit 3 occurring in them are :
03, 13, 23, 30, 31,32,33, 34, 35, 36, 37, 38, 39, ,43,53, 63, 73,83,93,
1 + 03,13, 23, 30, 31, 32, 33, 34,35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93,
2 +
3 +
4 + ...

so from 00 to 99: we have  20 of digit 3.
100 to 199             20      total      up to 199 : 40
200 to  299 :          20            total up to 299: 60
300 to  399 :          20 + 100    total up to 399 :  180

From 300: 309 :  we have 10    so total 70  of digit 3.
310 to 319 :            10 :              80
320 to 329 :            10:             90

So now,   330, 331, 332, 333, : there are 9 of the digit 3.