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Bosnia and Herzegovina JBMO TST 2013 Problem 4

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2013

September 16, 2018

combinatoricspolygonVertices

Problem Statement

It is given polygon with

2013

sides

A_{1}A_{2}...A_{2013}

. His vertices are marked with numbers such that sum of numbers marked by any

9

consecutive vertices is constant and its value is

300

. If we know that

A_{13}

is marked with

13

and

A_{20}

is marked with

20

, determine with which number is marked

A_{2013}