March 18, 2014

Problem of the Week

for Tuesday, March 18, 2014

For the second episode of the new quiz show called "Hats", three players make up a team. The game show host flips a coin three 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 two players' heads but not the one on her own head nor the result of the coin flip that preceded the placing of her hat. One of the three people on the team will then volunteer to guess her hat color. If she is right, her team wins, and if she is wrong, her team loses. If the three players are allowed to meet before hand to work out a strategy but are not allowed to communicate once the hats are placed , what strategy will guarantee them a higher than 50% chance of success? What is their probability of success?

Winners of the second episode