### Sperner's Lemma. What is it about? A Mathematical Droodle

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### Definition

A Sperner labeling of a triangle's triangulation is a labeling that satisfies the following conditions:

1. The vertices of the original triangle are labeled with three different letters A, B, and C.
2. Vertices of the triangulation that lie on the side AB are labeled either A or B. A similar condition holds for the vertices on sides BC and AC.
3. There is no restriction on labeling of the vertices of the triangulation inside the original triangle.

### Sperner's Lemma

Every Sperner's labeling contains at least one complete triangle.

Explanation