What color is my hat?

Logic Level 2

A police officer has caught four criminals and plays a game with them. They are not allowed to communicate with each other during the game but are allowed to discuss strategy before.

He lines up three of the prisoners (A, B, C) in one room, placing the fourth prisoner (D) in a separate room where he can hear the other three shout out. Each prisoner is given a hat to wear, blind-folded. The officer tells them that there are in total two blue hats and two red hats.

  • prisoner A can see the colors of the hats worn by prisoners B and C;
  • prisoner B can only see the color of the hat worn by prisoner C.

The game proceeds as follows:

  • In the first minute, Prisoner A's blindfold is opened. A can either guess the correct answer or say, I do not know the color of my hat.
  • In the second minute, Prisoner B's blindfold is opened and it's B's turn to guess.
  • In the third minute, Prisoner C's blindfold is opened and it's C's turn to guess.
  • In the fourth minute, Prisoner D's blindfold is opened and it's D's turn to guess.

The prisoners being perfect logicians, it is guaranteed that one of them can always guess his color accurately. Which one?


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