how many digits does it take in total to number a book from page 16 to page 667

how many digits does it take in total to number a book from page 16 to page 667
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The total number of pages to number is 667-16+1=652, the extra 1 being added because we have to include the last page (for example, pages 16 to 17 is 2 pages, but 17-16=1). We need 2 digits for pp 16 to 99, which is 84 pages and we need 3 digits for the remaining 652-84=568 pages. So that makes 84*2+568*3=168+1704=1872 digits.

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