$\textbf{Connect the Lights}$
You are in a control room which has three switches. Each switch controls one of three lights in another room. Once you leave the control room, you can not touch the switches again. How can you figure out which switch controls which light?
$\textbf{Solution}$
Turn on switch 1 and 2 for a while, and then turn off the switch 2. Afterwards, go to inspect the three lights in the other room. The light which is on connects to the $1^{st}$ switch. The light which is off but the bulb is warm connects to the $2^{nd}$ switch. And the light which is off and the bulb is cold connects to the $3^{rd}$ switch.
$\textbf{Analysis}$
This is not a pure math or logic quiz. A switch has only two states, on and off. Therefore, it is impossible to determine three relationships. In order to establish three relationships, we have to find a third indicator. In this case, it is a physical measurement, i.e. heat.