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The book that took 792 digits to number

countingdigitsarithmetic

A printer numbers the pages of a book from 1 upwards. When the job is finished, exactly 792 digits have been printed in total (a page numbered 123 uses three digits).

How many pages does the book have?

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Count the digits used by the one-digit pages, then the two-digit pages, and see how many are left for the three-digit pages.

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Balls and Bins and the Birthday ProblemBinomial Coefficients and Pascal's TriangleBurnside's Lemma and Polya CountingCatalan NumbersCounting: Permutations and Combinations

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