4
Part of 1985 Bundeswettbewerb Mathematik
Problems(2)
each point of the 3-dimensional space is coloured
Source: Bundeswettbewerb Mathematik 1985, first stage, problem 4
5/14/2004
Each point of the 3-dimensional space is coloured with exactly one of the colours red, green and blue. Let , and , respectively, be the sets of the lengths of those segments in space whose both endpoints have the same colour (which means that both are red, both are green and both are blue, respectively). Prove that at least one of these three sets includes all non-negative reals.
geometry3D geometryspheregeometry solved
512 persons meet at a meeting
Source: 1985 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p4
11/21/2022
persons meet at a meeting[ Under every six of these people there is always at least two who know each other. Prove that there must be six people at this gathering, all mutual know.
combinatorics