MathDB

A regular 1001-gon is drawn on a board, the vertiecs of which are numbered with

1,2,\ldots,1001.

Is it possible to label the vertices of a cardboard 1001-gon with the numbers

1,2,\ldots,1001

such that for any overlap between the two 1001-gons, there are two vertices with the same number one over the other? Note that the cardboard polygon can be inverted.

Problem Statement