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Part of 2013 Bosnia and Herzegovina Junior BMO TST

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Bosnia and Herzegovina JBMO TST 2013 Problem 4

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2013

9/16/2018
It is given polygon with 20132013 sides A1A2...A2013A_{1}A_{2}...A_{2013}. His vertices are marked with numbers such that sum of numbers marked by any 99 consecutive vertices is constant and its value is 300300. If we know that A13A_{13} is marked with 1313 and A20A_{20} is marked with 2020, determine with which number is marked A2013A_{2013}
combinatoricspolygonVertices