Difference between revisions of "1996 AIME Problems/Problem 12"

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== Problem ==
 
== Problem ==
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For each permutation <math>a_1,a_2,a_3,\cdots,a_{10}</math> of the integers <math>1,2,3,\cdots,10</math>, form the sum
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<math>|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|</math>.
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The average value of all such sums can be written in the form <math>\dfrac{p}{q}</math>, where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q</math>.
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== Solution ==
 
== Solution ==
 
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Revision as of 15:12, 24 September 2007

Problem

For each permutation $a_1,a_2,a_3,\cdots,a_{10}$ of the integers $1,2,3,\cdots,10$, form the sum

$|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|$.

The average value of all such sums can be written in the form $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

Solution

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See also

1996 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions