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__NOTOC__  __NOEDITSECTION__  <div class="frontlink" style="background-color:#204079; color:#ffffff; font-size: 110%; padding-left:15px; padding-right:15px; padding-bottom:10px;  margin-left: 5px; box-shadow: 2px 2px 6px #ccc;"> <span style="font-size: 200%">'''Welcome to the AoPS Wiki!'''</span>
 
   
 
   
The AoPS Wiki project is administered by the [[Art_of_Problem_Solving|<span style="color:#83a1d6;">Art of Problem Solving</span>]] for supporting educational content useful to avid math students.  The wiki will be in read-only mode through Wednesday, November 18th, 2015.
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The AoPS Wiki project is administered by the [[Art_of_Problem_Solving|<span style="color:#83a1d6;">Art of Problem Solving</span>]] for supporting educational content useful to avid math students.  The wiki will be in read-only mode through Wednesday, November 18th, 2015. Please do not discuss the 2015 AMC 8 Competition on any website until November 25th.
 
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Revision as of 17:10, 16 November 2015

Problem of the Week

1983 AIME, Problem 13

For $\{1, 2, 3, \ldots, n\}$ and each of its non-empty subsets a unique alternating sum is defined as follows. Arrange the numbers in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers. For example, the alternating sum for $\{1, 2, 3, 6,9\}$ is $9-6+3-2+1=5$ and for $\{5\}$ it is simply $5$. Find the sum of all such alternating sums for $n=7$.


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