MathDB

The vertices of a regular

2012

-gon are labeled

A_1,A_2,\ldots, A_{2012}

in some order. It is known that if

k+\ell

and

m+n

leave the same remainder when divided by

2012

, then the chords

A_kA_{\ell}

and

A_mA_n

have no common points. Vasya walks around the polygon and sees that the first two vertices are labeled

A_1

and

A_4

. How is the tenth vertex labeled?
Proposed by A. Golovanov

Problem Statement