windowless room math problem help

A windowless room has three identical light fixtures, each with an identical light bulb contained within. Each light is connected to one of the three switches outside of the room. Each bulb is switched off at present. You are outside the room, and the door is closed. You have one, and only one, opportunity to flip any of the external switches. After this, you can go into the room and look at the lights, but you may not touch the switches again. How can you tell which switch goes to which light?

Solution:

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