ASU 230 All Soviet Union MO 1976 dividing an equilateral into big triangles
Source:
July 6, 2019
Equilateralcombinatorial geometrycombinatorics
Problem Statement
Let us call "big" a triangle with all sides longer than . Given a equilateral triangle with all the sides equal to . Prove that: a) You can cut big triangles out of given one. b) You can divide the given triangle onto big nonintersecting ones fully covering the initial one. c) The same as b), but the triangles either do not have common points, or have one common side, or one common vertex. d) The same as c), but the initial triangle has the side .