518

Part of 1990 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 518 All Soviet Union 1990 n^2 equilateral triangle of side 1, acute in path

Source:

An equilateral triangle of side

n

is divided into

n^2

equilateral triangles of side

1

. A path is drawn along the sides of the triangles which passes through each vertex just once. Prove that the path makes an acute angle at at least

n

equilateralsacutecombinatorial geometrycombinatorics