There was once a reclusive inventor who became so annoyed with unwanted visitors ringing his doorbell that he decided to discourage them by inventing a new one.
The device consisted of a row of six push buttons mounted on the front door, wired in such a way that only one of the buttons would ring the bell. If an incorrect button was pressed (even simultaneously with the correct one) the bell would be temporarily deactivated.
Only his close friends were told the identity of the correct button. Everyone else had to deduce it from an inscription on the front door which read ‘Exactly one button is somewhere to the left of the one, that is three to the right of the one, that is somewhere to the right of the one, that is next to the one, that is two away from the one that is first mentioned. Ring the only button of the six that is not mentioned above.’
What was the position of the correct button?
The correct button is fifth from the left.
The inscription states that only one of the six buttons is not mentioned, so exactly five different buttons are mentioned. In the statement of relations between positions, the inscription refers to six buttons; however, the first and last mentioned buttons are the same one.
One now labels the buttons mentioned in the inscription in the order A B C D E A and begins by noting the most precise relation, that is, B is three to the right of C. Since no position may have two letters, our deductions show that from left to right the buttons are D E C A ? B. So the correct button must be the missing one.