A conference room has a pair of three-way switches for the overhead lights. One switch is located at the south entrance, and one is located at the north entrance. The south entrance is the one normally used, and typically that switch works as intended. For it to do so, however, the north switch has to be in the down position. If the north switch is in the up position, the south switch cannot turn off the lights.
Another odd thing is that the receptacle bank at the lectern works only with the north switch up. This means when the room is used for a presentation accompanied by a slide show, the meeting coordinator has to remember to flip both switches up at the start and both down at the end. This seems to defeat the purpose of having three-way switches. How might you fix this?
Lockout/tagout the supply breaker to the lighting circuit. Without disconnecting any wires, pull each switch out. Label the wires in some way if they are not already labeled. Write down which wire goes to which terminal. Disconnect the wires.
Close the breaker. Now with power on, use an inductive voltage tester to identify the hot wire at each switch. This must go to the correct terminal on the switch. You will notice that two terminals are the same color (probably a light bronze). The traveler (non-hot) wires go to these terminals, and it doesn’t matter which one goes where. The dark-colored screw is the hot terminal, the one that the hot wire goes to.
The behavior described is a classic sign of miswiring. Connect the hot to the correct terminal, and the problems should be solved.