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Solution to: Missing Pages

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 × (2p + n + 1) / 2 = 2 × 2 × 2 × 2 × 613

So:

n × (2p + n + 1) = 2 × 2 × 2 × 2 × 2 × 613

One of the two terms n and 2p + n + 1 must be even, and the other one must be odd. Moreover, the term n must be smaller than the term 2p + n + 1. It follows that there are only two solutions:

Because it is asked which pages (plural) are missing, the solution is: the pages 291 up to and including 322 are missing.


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