Beach Day by Rodger Bliss
May 2024

Mean Spirited Warden

A warden meets with 23 new prisoners when they arrive. He tells them, “You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

“In the prison is a switch room, which contains two light switches labeled A and B, each of which can be in either the ‘On’ or the ‘Off’ position. I am not telling you their present positions. The switches are not connected to anything.

“After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must move one, but only one of the switches. He can’t move both but he can’t move none, either. Then he’ll be led back to his cell.

“No one else will enter the switch room until I lead the next prisoner there, and he’ll be instructed to do the same thing. I’m going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back.

“But, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time anyone of you may declare to me, ‘We have all visited the switch room.’

“If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will be fed to the alligators.”

Here’s the question:

What is the strategy the prisoners devise?

And here are the hints I’ll give:

Hint number 1: A sixth grader could figure this puzzler out.

Hint 2: Take a long-term perspective.

And Hint 3: Solve the puzzler for three prisoners–it’s the same answer

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2 guesses to Mean Spirited Warden

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  • Paul

    The prisoners pick one lead guy that is in charge of counting and resetting the control switch. Each prisoner is told to click the switch on the left to the off position twice, and only twice. If they arrive in the room and the left switch is already off or if they’ve already clicked it off twice, they click the right switch. The right switch is the throw away switch because only the left switch matters. When the lead guy goes into the room, if the left switch is off, he knows one of the prisoners clicked it off and he resets it by turning it on. He keeps track of the number of times the left switch is in the off position until the count reaches 44, meaning all 22 prisoners plus himself had been in the room. Because the warden tells them he’s not going to tell them the position of the two switches, the leader/counter won’t know if it started in the off position. This is why each prisoner needs to click the left switch off twice.

    Hint – a sixth grader, really? That’s a hint, really? Why not a second grader? Or a bonobo? If fruit flies could communicate, I suppose they’d figure this out too?

  • Great job, Paul.

    You explained it perfectly.

    By the way, during test studies, the Pygmy Chimps couldn’t solve the riddle.

    You’re today’s winner.