Puzzle: Placed in a room without mirrors are three males who are not wearing glasses. They are each given a headgear that they are unable to see. The color of the hat is either red or green. They are not permitted to look at their own hats in any way, and they are not allowed to speak or interact with each other in any way other than by raising their right hands in the event that they see a red hat. They are instructed to leave the room quickly without saying anything to anyone if they are able to identify the color of their own hat. How did he figure out what color his own hat was?
Hats in a Circle
Solution:
If you are placed in a room with two other people and each of you is wearing a hat that is either red or green, but you are not allowed to look at your own hat or communicate with the others in any way, how can you figure out the color of your own hat?
One solution to this problem is to use a process of elimination. For example,
- let’s say that you are the first person in the room. You cannot see your own hat, but you can see the hats of the other two people. If one of them is wearing a red hat, you can raise your hand to signal that you see a red hat. If both of the other people are wearing green hats, then you know that your own hat must be red, since there are only two colors of hats and one of them must be on your head.
- Now let’s say that the second person in the room sees a red hat. They will raise their hand to signal this, and you will know that the third person’s hat must be red as well. This means that your own hat must be green since there are only two colors of hats and one of them is on your head.
- In this way, each person in the room can use the information provided by the others to deduce the color of their own hat without ever looking at it or communicating directly with the others.
Representation of the solution
Of course, the solution requires that at least one person in the room is wearing a red hat. If everyone’s hat is green, then it will not be possible for any of the people in the room to figure out the color of their own hat using this method. However, it is still possible for them to figure it out by using other strategies, such as trying to infer the color of their hat based on the colors of the hats worn by the other people in the room.