4. In a coffee shop, 55 Indians and Turks met, each drinking tea or coffee. All Indians tell the truth when drinking tea and lie when drinking coffee, while all Turks do the opposite. When asked "Are you drinking coffee?" 44 people answered "yes," when asked "Are you a Turk?" 33 people answered "yes," and 22 people agreed with the statement "It is raining outside." How many Indians in the coffee shop are drinking tea?
Answer: 0. Solution. Let $h_{\psi}, h_{\kappa}$ be the number of Indians drinking tea and coffee, respectively. Similarly, define the quantities $T_{4}$ and $T_{k}$. Then from the first question, it follows that $T_{4}+T_{\kappa}=44$, and from the second question, it follows that $h_{\kappa}+T_{\kappa}=33$. Suppose that "It is raining outside" is a false statement. Then $h_{k}+T_{4}=22$. Adding the first two equations and subtracting the third, we get $2 T_{\kappa}=55$, a contradiction. Therefore, it is raining, from which $h_{4}+T_{\kappa}=22$. Adding all three equations and subtracting the obvious equation $h_{4}+h_{k}+T_{4}+T_{\kappa}=55$, we get $2 T_{\kappa}=44$, from which $T_{\kappa}=22$ and $h_{4}=0$.