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Good n-numbers - Iran NMO 1998 (Second Round) Problem3

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October 4, 2010
combinatorics proposedcombinatorics

Problem Statement

Let nn be a positive integer. We call (a1,a2,⋯ ,an)(a_1,a_2,\cdots,a_n) a good n−n-tuple if ∑i=1nai=2n\sum_{i=1}^{n}{a_i}=2n and there doesn't exist a set of aia_is such that the sum of them is equal to nn. Find all good n−n-tuple. (For instance, (1,1,4)(1,1,4) is a good 3−3-tuple, but (1,2,1,2,4)(1,2,1,2,4) is not a good 5−5-tuple.)
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