ISL 1970 Problem 13

Each side of an arbitrary $\triangle ABC$ is divided into equal parts, and lines parallel to $AB,BC,CA$ are drawn through each of these points, thus cutting $\triangle ABC$ 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 $1,2,3$ .