6) A rectangular room has walls facing the four cardinal directions and there are four access doors. Three people are in the room and make the following statements. First person: "There are no doors on the South wall". Second person: "There are doors only on the North wall". Third person: "There is at most one door on each wall". What can be said for certain about the statements made?

(A) The statement made by the first person is true, (B) The statement made by the second person is true, (C) The statement made by the third person is true, (D) At least one statement is false, (E) Nothing can be said for certain about the statements made.
6. The answer is (D). The statements of the second person and the third person are in contradiction with each other, so one of them must be false; therefore, there is at least one false statement. We also observe that the data in the problem does not imply that any of the statements made are necessarily true, so answers (A), (B), and (C) are not correct.