Školjka IMO Shortlist 1966 problem 43
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Given 
points in a plane, no three of them being collinear. Each two of these points are joined with a segment, and every of these segments is painted either red or blue; assume that there is no triangle whose sides are segments of equal color.
a.) Show that:
(1) Among the four segments originating at any of the points, two are red and two are blue.
(2) The red segments form a closed way passing through all given points. (Similarly for the blue segments.)
b.) Give a plan how to paint the segments either red or blue in order to have the condition (no triangle with equally colored sides) satisfied.
points in a plane, no three of them being collinear. Each two of these points are joined with a segment, and every of these segments is painted either red or blue; assume that there is no triangle whose sides are segments of equal color. a.) Show that:
(1) Among the four segments originating at any of the
points, two are red and two are blue. (2) The red segments form a closed way passing through all
given points. (Similarly for the blue segments.) b.) Give a plan how to paint the segments either red or blue in order to have the condition (no triangle with equally colored sides) satisfied.
Izvor: Međunarodna matematička olimpijada, shortlist 1966