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Puzzle Details

I am compiling the new BrainBashers world almanac and it now contains lots more pages.

I know that it takes 333 digits to print the page numbers in sequence.

How many numbered pages does the book have and how many times does the number 3 appear?

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.

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