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===Miscellaneous===
 
===Miscellaneous===

Revision as of 08:55, 9 August 2020




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Welcome to Aops-g5-gethsemanea2's Wiki!

Aops-g5-gethsemanea2's Wiki project is administered by the user Aops-g5-gethsemanea2 for supporting educational content useful to avid math students.

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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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