  Entanglement is perhaps the most non-classical manifestation of quantum
mechanics. Among its many interesting applications to information processing,
it can be harnessed to reduce the amount of communication required to process a
variety of distributed computational tasks. Can it be used to eliminate
communication altogether? Even though it cannot serve to signal information
between remote parties, there are distributed tasks that can be performed
without any need for communication, provided the parties share prior
entanglement: this is the realm of pseudo-telepathy.
  One of the earliest uses of multi-party entanglement was presented by Mermin
in 1990. Here we recast his idea in terms of pseudo-telepathy: we provide a new
computer-scientist-friendly analysis of this game. We prove an upper bound on
the best possible classical strategy for attempting to play this game, as well
as a novel, matching lower bound. This leads us to considerations on how well
imperfect quantum-mechanical apparatus must perform in order to exhibit a
behaviour that would be classically impossible to explain. Our results include
improved bounds that could help vanquish the infamous detection loophole.
