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 Missing Pages (Posted on 2009-11-13)
A chunk of pages is missing from a book. The sum of the missing page numbers is 9808. What are those page numbers?

 See The Solution Submitted by Brian Smith Rating: 3.5000 (2 votes)

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 Spreadsheet Solution | Comment 6 of 7 |
For an even sum the pages  must be multiples of 4 and in the order of odd-even.

The sum of pages is given by the triangular sequence N*(N+1)/2 while the sequence of sums of multiples of 4 is given by 8N^2+2N.

At any point "y" the sum may be expressed by a triangular number plus a constant [K] and the sum at the next term "y+1" will be the next triangular number plus K.

Using those principles in a spreadsheet and by reiteration I subtracted successive 4N multiples from 9808 and then divided by 4N.  If the quotient was an integer then I would have K.  The missing pages would therefore be from K+1 to K+4N.

4N    N    8N^2+2N                           K
4      1      10          9808    9798    2449.5
8      2      36          9808    9772    1221.5
12    3      78          9808    9730    810.8333
16    4    136          9808    9672    604.5
20    5    210          9808    9598    479.9
24    6    300          9808    9508    396.1667
28    7    406          9808    9402    335.7857
32    8    528         9808    9280     290
36    9    666         9808    9142     253.9444

The integer K occurs for 4N=32 so the pages are from 291 to 322.

 Posted by brianjn on 2009-11-13 21:37:44

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