1996 AIME Problems/Problem 12: Difference between revisions
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== Problem == | == Problem == | ||
{{ | 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 | ||
<math>|a_1-a_2|+|a_3-a_4|+|a_5-a_6|+|a_7-a_8|+|a_9-a_{10}|</math>. | |||
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>. | |||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
Revision as of 15:12, 24 September 2007
Problem
For each permutation 
of the integers 
, form the sum
.
The average value of all such sums can be written in the form 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
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See also
| 1996 AIME (Problems • Answer Key • Resources) | ||
| 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 | ||
