1995 segments such that any 3 of them form a triangle
Source: I Soros Olympiad 1994-95 Ukraine R2 10.4 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
June 6, 2024
combinatoricsgeometrycombinatorial geometry
Problem Statement
There are 1995 segments such that a triangle can be formed from any three of them. Prove that using these segments, it is possible to assemble acute-angled triangles so that each segment is part of no more than one triangle.