We were talking to Charlie Panoff from Objective Solutions International about hedge fund job interviews and he asked us this question – and, for the record, no we did not get it right. Hopefully, you’ll be better prepared and when asked this one, a lightbulb will go on.
Q: A windowless room contains three identical light fixtures, each containing an identical light bulb. Each light is connected to one of three switches outside of the room. Each bulb is switched off to begin. You are outside the room, the door is closed, you can not see anything inside the room. You have one, and only one, opportunity to flip any of the external switches. After flipping your chosen switch(es), you may go into the room and look at the lights. You may not touch the switches again. How can you tell which switch goes to which light?
A: Turn on switch #1 for a short while, then turn it off. Turn on switch #2 and immediately enter the room.
The illuminated bulb represents switch #2. The warm but turned off bulb represents switch #1. The cold, non-illuminated bulb represents switch #3.
Note: This solution works if at the beginning all bulbs are off. What if they are all on? You won’t be able to tell from the heat, so just guess. You have a 1 in 6 chance if they are random, however, most light switches/fixtures are not random. Your chances improve based on standard configurations.
Although we learned of this question in our interview with Charlie Panoff, we found it in written form in Timothy Crack’s Heard on the Street: Quantitative Questions from Wall Street Job Interviews. Buy the book for more questions like these.