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Friday, March 9, 2012

Friday Puzzle

 A book contains N pages, numbered, per usual, from 1 to N, with the total number of digits in those page numbers equal to 1095 (i.e. 1095 individual numbers). That being the case, how many pages are in the book?

Answer below:

(...and on a sidenote, worth mentioning that Salmon Khan, founder of Khan Academy, will be the focus of a segment of "60 Minutes" this coming Sunday.)
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ANSWER:  Every page will have at least one digit, so that's N digits right off the bat. All but the first 9 pages will have 2 digits so that N - 9 will have a second digit. And finally, by the same logic, there will be N - 99 3rd digits. Thus 1095 must equal N + (N - 9) + (N - 99) or 3N - 108. Working out the equation N = 401 pgs.

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