MathDB

Let

n\geq 3

be an integer. We say that a vertex

A_i (1\leq i\leq n)

of a convex polygon

A_1A_2 \dots A_n

is Bohemian if its reflection with respect to the midpoint of

A_{i-1}A_{i+1}

(with

A_0=A_n

and

A_1=A_{n+1}

) lies inside or on the boundary of the polygon

A_1A_2\dots A_n

. Determine the smallest possible number of Bohemian vertices a convex

n

-gon can have (depending on

n

).
Proposed by Dominik Burek, Poland

Problem Statement