4. In a room, 13 chairs are arranged in a row. Three jewelers sit on three adjacent chairs, and the middle one hides a diamond in the chair he is sitting on. The inspector has six detectors that show whether someone has sat on a chair or not. Can he place the detectors on the chairs before the jewelers arrive so that their readings can determine where the diamond is?
Answer: can.

Instruction. Layout: s s d d d s s d d d s s (s - chair without detector, d - chair with detector). Since there are no three empty (without detectors) chairs in a row, at least one of the detectors will go off. If one goes off, then they were sitting on the chair with the triggered detector and on the two adjacent chairs without detectors. If two go off, then they were sitting on these chairs and the adjacent one without a detector. If three go off, then they were sitting on these. Knowing the chairs they were sitting on, we choose the middle one.

Criteria. Correct placement of detectors without explaining how to find the chairs they were sitting on: 5 points.