Dissect a triangle into smaller triangles, such that all have full edge contact with their neighbors. Label the corners 1, 2, and 3. Label all vertices with 1, 2, or 3, with a restriction that the vertices of the side opposite a number lack that number. Thus, the side opposite 1 contains no vertices labelled 1.
Then Sperner's lemma states that any such labelling must contain an odd number of triangles with vertices labelled 1, 2, 3.
