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3

Part of 2005 Turkey Junior National Olympiad

Problems(1)

Turkey Junior Olympiad 2005, Part II - P3

Source:

1/20/2013
Determine whether or not there exists a sequence of integers a1,a2,…,a19,a20a_1,a_2,\dots, a_{19}, a_{20} such that, the sum of all the terms is negative, and the sum of any three of the terms is positive.