March 24, 2014

Problem of the Week

for Tuesday, March 24, 2014

For the third episode of the new quiz show called "Hats", four players make up a team. The game show host flips a coin four times to determine the color of the hat to be placed on each person's head. When a heads is flipped the hat is white, and when a tails is flipped the hat is black. Each player sees the hats on the other three players' heads but not the one on her own head nor the result of the coin flip that preceded the placing of her hat. If the four players are each given a stop-watch and twenty seconds for one of them to make a guess, what strategy can they work out in advance of the play that will guarantee them a higher than 75 percent chance of success? What is their chance of success?

Winners of the third episode