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Problem 1

Part of 1997 French Mathematical Olympiad

Problems(1)

labelling vertices of 1997-gon

Source: French MO 1997 P1

4/10/2021
Each vertex of a regular 19971997-gon is labeled with an integer, so that the sum of the integers is 11. We write down the sums of the first kk integers read counterclockwise, starting from some vertex (k=1,2,…,1997)(k=1,2,\ldots,1997). Can we always choose the starting vertex so that all these sums are positive? If yes, how many possible choices are there?
combinatorics