  In the Proceedings of the AMS Boulder conference in 1965 Langlands states a
combinatorial lemma involving families of characteristic functions attached to
ordered partitions of an obtuse basis in a finite dimensional euclidean vector
space. Langlands does not give any indication about the proof of the lemma
which is said to be a "pleasant exercise". Since we did not find a proof in the
literature we decided to give one. We believe it of some interest for the
history of the subject.
