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Circle Labeled Integers Maximum Positives

2300ExpertCombinatoricsSequences & Series

49th Austrian Mathematical Olympiad, National Competition (Final Round, part 2)

On a circle 2018 points are marked. Each of these points is labeled with an integer. Let each number be larger than the sum of the preceding two numbers in clockwise order. Determine the maximal number of positive integers that can occur in such a configuration of 2018 integers.
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