6

Part of 1991 Mexico National Olympiad

Problems(1)

set Τ: Every two triangles in T have either two common vertices, or none.

Source: Mexican Mathematical Olympiad 1991 OMM P6

n

n\ge 4

), consider a set

T

of triangles formed by vertices of the polygon having the following property: Every two triangles in T have either two common vertices, or none. Prove that

T

contains at most

n

combinatorial geometrygeometryset