Brain Challenge: Can You Solve The Red & Green Hat Puzzle?

4 years ago



Attention all fashionistas! It’s time for some puzzle solving. Today, it’s a puzzle with a twist to get your brains out of neutral. Ready! Steady! Go!


Riddle lovers might remember a good old puzzle dating back to the 1940s. The initial version involved three logicians, who would randomly take a hat out of the box and put it on, eyes closed. Next, eyes open, each needed to conclude which color they are wearing based on the hats seen on their fellow logicians.  


The modern-day’s puzzle has an unexpected twist with one of the participants being colorblind! So, there’s a box containing 2 red hats and 3 green hats.


Kate, Wilson and James close their eyes, each take out a hat from the box and put it on. After they open their eyes, they see the hats worn by others, but not their own. But they don’t know what color hats are left in the box.


The conditions of the puzzle are as follows:

  • All the participants are perfect logicians telling the truth.
  • They know all the information in the above paragraph.
  • In addition, one of them is colorblind, and all of them know who that person is.

Kate says: “I don’t know the color of my hat.”

Wilson says: “I don’t know the color of my hat.”

James says: “I don’t know the color of my hat.”

Kate says: “I don’t know the color of my hat.”


Who is the colorblind person, and what color hat are they wearing?


The Solution of The Red & Green Hat Puzzle


1. For starters, let’s presume what would have happened if none of the participants were colorblind.


The only way for Kate to find out the color of her hat is when both Wilson and James are wearing red hats. Then, she would deduce all red hats are taken and so hers must be green.


However, Kate doesn’t know what hat color she’s wearing, so presumably she is cannot see two red hats on the other two participants. Hence, she sees either two greens, or a red and a green.


And now to Wilson, who presumably knows about this. Suppose he sees James wearing a red hat, so it’s possible that he would deduce he’s wearing a green hat, knowing that Kate can only see one red hat. Since Wilson has no idea what color hat he’s wearing, let’s eliminate the possibility of James having a red hat.


The conclusion is as follows: both Kate and Wilson have said they don’t know their hat color, but everyone knows that James has a green hat (including himself).


2. Let’s presume one of the participants is colorblind.


Now we know that James isn’t the one. Why? Because if Kate and Wilson can see colors, then James will deduce what color hat he’s wearing even if colorblind.


Kate cannot be colorblind either, because if she was, her first statement is meaningless. Obviously, she doesn’t know what  color hat she’s wearing, she’s colorblind!


As soon as Wilson and James say they don’t know the color of their hats, everyone knows that Kate has a green hat (including herself). So, if you follow the above explanation, Kate would not say she has no idea what color of her hat is for the second time.


And, the colorblind person is Wilson and given the other two participants have no idea what color hats they’re wearing, most certainly he has a green hat.


Hopefully, you loved the puzzle! See you next time.


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Any questions or propositions?