IMO Shortlist 2002 problem C1
Kvaliteta:
Avg: 4.0Težina:
Avg: 6.0 Let
be a positive integer. Each point
in the plane, where
and
are non-negative integers with
, is coloured red or blue, subject to the following condition: if a point
is red, then so are all points
with
and
. Let
be the number of ways to choose
blue points with distinct
-coordinates, and let
be the number of ways to choose
blue points with distinct
-coordinates. Prove that
.
















Source: Međunarodna matematička olimpijada, shortlist 2002