Tuesday Teaser #25
This week’s (very tough) teaser is taken from the New York Times’ excellent Numberplay series:
Many years ago, six people — Alfred Dreyfus, Jean Calas, Emile Outreau, Jeanne d’Arc, François Outreau and Nicolas Bourbaki — were sentenced to solitary confinement in a French prison — unfairly, many thought. Fortunately, they had a sympathetic warden, who gathered them together in the prison yard and said: “It is widely felt that you were victims of miscarriages of justice. So I’ll give you some hope of getting free. You will each be taken, one by one, in a pre-set order you will all be told, to a room which has a set of six card drawers. Each drawer has a single card in it, bearing one of your names, placed in random order. Each of you can open any three drawers of your choice. Your goal is to find the card that has your name. After you have left the room, everything will be returned to the way it was for the next person, and you will be returned to your solitary cell, unable to communicate with any of the others. If every one of you succeeds independently in finding your own card, then all of you will be set free. If even a single one fails, you will all remain prisoners. The odds are very small, but that’s the best I can do. You are free to discuss this amongst yourselves just now, and come up with a good strategy.” With that, he left, giving them a few hours together to make a plan.
“We don’t have much hope,” said one of the Outreaus, a primary school teacher. “If we each choose at random, the chances are just 1 in 64 that we’ll all find our names.” “No,” said Nicolas Bourbaki excitedly, “we can do much, much better.” (Bourbaki was an accomplished mathematician who had been convicted on several counts of identity theft). “We have close to a 40 percent chance of being freed,” he said. “Here’s what we need to do … ”
What was Bourbaki’s strategy?
