The numbers from 1 to $n$ are arranged in some way on a circle. What’s the smallest value of $n$, for which no matter how the numbers are arranged there exist ten consecutively increasing numbers $A_1<A_2<A_3…<A_{10}$ such that $A_1 A_2…A_{10}$ is a convex decagon?
Problem
Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade
Tags: combinatorial geometry, combinatorics