  Pseudo-telepathy is the most recent form of rejection of locality. Many of
its properties have already been discovered: for instance, the minimal
entanglement, as well as the minimal cardinality of the output sets, have been
characterized. This paper contains two main results. First, we prove that no
bipartite pseudo-telepathy game exists, in which one of the partners receives
only two questions; as a corollary, we show that the minimal "input
cardinality", that is, the minimal number of questions required in a bipartite
pseudo-telepathy game, is 3x3. Second, we study the Bell-type inequality
derived from the pseudo-telepathy game known as the Magic Square game: we
demonstrate that it is a tight inequality for 3 inputs and 4 outputs on each
side and discuss its weak resistance to noise.
