MathDB

There is convex

n-

gon. We color all its sides and also diagonals, that goes out from one vertex. So we have

2n-3

colored segments. We write positive numbers on colored segments. In one move we can take quadrilateral

ABCD

such, that

AC

and all sides are colored, then remove

AC

and color

BD

with number

\frac{xz+yt}{w}

, where

x,y,z,t,w

- numbers on

AB,BC,CD,DA,AC

. After some moves we found that all colored segments are same that was at beginning. Prove, that they have same number that was at beginning.

Problem Statement