The issue of adequacy of the Turing Test (TT) is addressed. The concept of Turing Interrogative Game (TIG) is introduced. We show that if some conditions hold, then each machine, even a thinking one, loses a certain TIG and thus an instance of TT. If, however, the conditions do not hold, the success of a machine need not constitute a convincing argument for the claim that the machine thinks. Keywords Turing test Á Logic of questions Á Interrogative games Á Recursion theory The Turing Test Despite its years, the Turing Test (TT) still brings in new issues, and the dispute over it is far from being closed; see for example the latest collection of papers (Epstein et al. 2009). One of the central topics in this area is the problem of adequacy of TT as a tool for investigating if artificial agents think. 1 Our aim is to address this issue by using a certain formal approach. Papers devoted to TT most often are philosophical in nature and methods used. Among recent papers notable exceptions are: Turing Machines approach (Sato and Ikegami 2004), exploring the computational complexity of TT setting (Hernandez-Orallo 2000), applying the interactive proof theory in modeling TT (Bradford and