4
Part of 1976 Bundeswettbewerb Mathematik
Problems(2)
at most 3n-6 segments by n distinct points under conditions
Source: 1976 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p4
11/20/2022
In a plane are given distinct points. Some pairs of these points are connected by segments so that no two of the segments intersect. Prove that there are at most segments.
geometrycombinatoricscombinatorial geometry
Euclidean space
Source: Bundeswettbewerb Mathematik 1976, second round, problem 4
11/8/2003
Each vertex of the 3-dimensional Euclidean space either is coloured red or blue. Prove that within those squares being possible in this space with edge length 1 there is at least one square either with three red vertices or four blue vertices !
geometry3D geometryspheregeometric transformationvectorcombinatorics solvedcombinatorics