Each side of an arbitrary △ABC is divided into equal parts, and lines parallel to AB,BC,CA are drawn through each of these points, thus cutting △ABC into small triangles. Points are assigned a number in the following manner:
(1) A,B,C are assigned 1,2,3 respectively
(2) Points on AB are assigned 1 or 2
(3) Points on BC are assigned 2 or 3
(4) Points on CA are assigned 3 or 1
Prove that there must exist a small triangle whose vertices are marked by 1,2,3. geometry unsolvedgeometry