« Vrati se
Given 5 points in a plane, no three of them being collinear. Each two of these 5 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 5 points, two are red and two are blue.

(2) The red segments form a closed way passing through all 5 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.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1238IMO Shortlist 1966 problem 550
1236IMO Shortlist 1966 problem 530
1230IMO Shortlist 1966 problem 470
1224IMO Shortlist 1966 problem 410
1215IMO Shortlist 1966 problem 320
1186IMO Shortlist 1966 problem 31