2

Part of 2004 Chile National Olympiad

Problems(1)

all points on line, red or blue

Source: Chile Finals 2004 L2 p2

Every point on a line is painted either red or blue. Prove that there always exist three points

A,B,C

that are painted the same color and are such that the point

B

is the midpoint of the segment

AC

combinatoricspointsColoringcombinatorial geometry