In a wood-cutting factory, four large sawing machines stand in a windowless room. Each machine has an on/off switch attached, there being no doubt as to which switch controls which machine. Outside the door to the room are four back-up on/off switches, one for each machine inside. The power for each machine must first pass through the back-up switch, and then the machine switch before reaching the saw. The problem is, the new manager cannot decide how these back-up switches match with the machines inside the room. One day, the manager's brother visits. The manager takes him inside the sawing room where all four machines are at work and explains the problem. The brother announces that he intends to leave the room and that when he returns he will be able to match correctly the four switches outside the room to the four machines inside. The brother works alone, cannot see the machines from outside the room and solves the problem purely by operating switches. How is it possible?