I was always fascinated with this result. Sperner's lemma is a combinatorial result which can prove some pretty strong facts, as Brouwer fixed point theorem. I know at least another application of this lemma, namely, Monsky's theorem, which states that it is impossible to dissect a square into an odd number of triangles having equal areas.
Browsing through a few questions this evening I found two references to Sperner's lemma with respect to totally different applications. I searched the site, and didn't found a question which asks about other applications of Sperner's lemma, so I thought I'll ask the question myself.
What other applications of Sperner's lemma are there?
(I made the question community wiki.)