MathDB

Let

ABCDEFG

be a regular heptagon. We'll call the sides

AB

BC

CD

DE

EF

FG

and

GA

opposite to the vertices

E

F

G

A

B

C

and

D

respectively. If

M

is a point inside the heptagon, we'll say that the line through

M

and a vertex of the heptagon intersects a side of it (without the vertices) at a

<span class='latex-italic'>perfect</span>

point, if this side is opposite the vertex. Prove that for every choice of

M

, the number of

<span class='latex-italic'>perfect</span>

points is always odd.

Problem Statement