Hint: Think of the pages from 1-9, and then 10-99.

Answer: There are 147 pages and the number 3 appears 35 times.

Stage 1
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For pages 1 - 9 we have a total of 9 digits. For pages 10 - 99 we have a total of 180 digits. This is a total so far of 189, therefore we require another 144 digits, which is another 48 pages. Taking us to 147 pages in total.

Stage 2
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From page 1 to 147 we have 15 times where the page number ends in 3. We also have the ten pages in the 30's, and the ten pages in the 130's that have the extra 3 in them. For a total of 35 number 3s.