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# Book, Math Puzzles

From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808. Which pages are missing?

## Answers : Math Puzzles and Riddles

 Let the number of missing pages be n and the first missing page p+1. Then the pages p+1 up to and including p+n are missing, and n times the average of the numbers of the missing pages must be equal to 9808:    n*( ((p+1)+(p+n))/2 ) = 9808 In other words:    n*(2*p+n+1)/2 = 2*2*2*2*613 So:    n*(2*p+n+1) = 2*2*2*2*2*613       One of the two terms n and 2*p+n+1 must be even, and the other one must be odd. Moreover, the term n must be smaller than the term 2*p+n+1. It follows that there are only two solutions:       n=1 and 2*p+n+1=2*2*2*2*2*613, so n=1 and p=9808, so only page 9808 is missing.       n=2*2*2*2*2 and 2*p+n+1=613, so n=32 and p=290, so the pages 291 up to and including 322 are missing.       Because it is asked which pages (plural) are missing, the solution is: the pages 291 up to and including 322 are missing.

From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808. Which pages are missing?

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