Question 1150802
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If you look at the digit placeholders
[]      []      []
100's   10's    1's


For pages 1-100, she will need 10+10 = 20   "3"'s 
For pages 101-200, she will need an additional 20  "3"'s

If we take away pages 193, 183, and 173  she uses 37 "3"'s.

Thus, the maximum page number with 37 "3"'s as the limiting factor is  {{{ highlight( 172 ) }}}.