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Problem 1 of Third round - Convex decagons

Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade

September 1, 2019
combinatorial geometrycombinatorics

Problem Statement

The numbers from 1 to nn are arranged in some way on a circle. What’s the smallest value of nn, for which no matter how the numbers are arranged there exist ten consecutively increasing numbers A1<A2<A3…<A10A_1<A_2<A_3…<A_{10} such that A1A2…A10A_1 A_2…A_{10} is a convex decagon?
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