MathDB

1993 points in each quadrant of the circle

Source: IMO Shortlist 1993, Brasil 1

March 14, 2006

algebrageometrypoint setdistancecombinatorial geometryIMO Shortlist

Problem Statement

Show that there exists a finite set

A \subset \mathbb{R}^2

such that for every

X \in A

there are points

Y_1, Y_2, \ldots, Y_{1993}

A

such that the distance between

X

and

Y_i

is equal to 1, for every

i.