5 Jul 2012

Light Bulb

This summer, we have to interview students applying for our medical school. GW suggested that I should ask the light bulb question. HC and RL were very curious and urged me to share it.

Here it goes.

There are 50 prisoners on life sentence at a remote island. Each of them occupies a separate cell in jail and cannot see or talk to each other. One day, the jail officer decides to play a game with them.

“From tomorrow onwards,” he explains, “I will reshuffle the cells you live in randomly every day. All but one cell are identical. In the special cell, which I would call Cell X, you are free to turn the light on and off at your will. You can only communicate with your fellow prisoners by switching the light bulb on or off, and are not allowed to leave other signals. If one day one of you can confidently claim that all 50 fellow prisoners have already been in Cell X at least once, I will set you all free. If, however, you make this claim but one or more prisoner has yet to enter Cell X, I will execute you all. Now, discuss the plan among yourselves. Good luck, gentlemen!”

Can you devise a plan to win this game?

After I had finished, HC and RL became very silent.

“We can draw lines on the wall,” RL finally muttered.

“Or we can leave our clothes in Cell X,” HC said.

“We’d better kill the officer while we are still together,” RL added.

And then they suggested 5 to 6 more possibilities.

“Hey,” I said, “neither of you are going to touch the light switch at all?”

“Can’t figure that out,” RL protested, “but shouldn’t the university encourage thinking outside the box?”

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