March 31, 2014
Problem of the Week
for Tuesday March 31, 2014
On the last episode of the first season of "Hats", four players comprise a team. The game show host places a white or black hat on each player's head. Each can see the other player's hat but not her own. They are told by the host that at least one of them has a black hat on. To win this competition, everyone on the team must guess the correct color of her hat. Each is given a control panel that features a clock, a switch to indicate her guess, and a set of three lights that turn on individually when each of the other three have made their guess. If the team is allowed to meet beforehand to work out a strategy, what strategy can they form that will allow all of them to make the correct guess in the twenty seconds that they are allotted? Players can send each other no signals other than those that are provided on the control panel.