This paper explores certain issues concerning the Turing test; non-termination, asymmetry and the need for a control experiment. A standard diagonalisation argument to show the non-computability of AI is extended to yields a socalled “April fool Turing test”, which bears some relationship to Wizard of Oz experiments and involves placing several experimental participants in a symmetrical paradox – the “April Fool Turing Test”. The fundamental question which is asked is whether escaping from this paradox is a sign of intelligence. An important ethical consideration with such an experiment is that in order to place humans in such a paradox it is necessary to fool them. Results from an actual April Fool Turing Test experiment are reported. It is concluded that the results clearly illustrate some of the difficulties and paradoxes which surround the classical Turing Test.