# A 3-person hat puzzle (no, not that one) (no, not that one either!)

No, this puzzle isn't a duplicate of any of the well-known hat puzzles we all know. Yes, it does have a valid solution. This puzzle was originally composed by Jack Lance and posted to a friend group with different names.

Deusovi, Rubio, and Boboquack are standing in a circle. From a bag of 2 red hats and 3 green hats, I put 1 hat on each person's head. They can each see each other's hats, but not their own. They also all know all this information.

The person on the left says, "I don't know what color hat I'm wearing".
The person in the center says, "I don't know what color hat I'm wearing".
The person on the right says, "I don't know what color hat I'm wearing".
The person on the left says (again), "I don't know what color hat I'm wearing".

Where is Deusovi standing, and what color hat is he wearing?

• VTC: primarily opinion-based, as the puzzle asserts I would ever stand in close proximity to Deusovi and Boboquack. ;)
– Rubio
Commented May 20, 2017 at 1:02
• excellently entertaining Commented Dec 4, 2019 at 8:20

## 1 Answer

The crucial fact here (which I think makes the question kinda unfair since it's not exactly common knowledge) is that

Deusovi is colour-blind. (Remark: I haven't checked that the other two aren't, but I hope OP has.)

And we had better

suppose that he is genuinely unable to distinguish the red and green hats from one another, which of course wouldn't necessarily be so in real life. And we'd better also assume that everyone involved knows this.

Now,

as soon as two people with normal colour vision have said "I don't know what color hat I'm wearing", all of them can reason as follows. If the first saw two red hats they'd know their hat was green. Therefore #1 sees at least one green hat, and everyone knows this. If #2 sees a red hat on #3, then the green hat seen by #1 would have to be on #2, and they would know their hat was green. So now we know that #3's hat is green.

So

if Deusovi is on the left, then his final statement would be wrong. (And Deusovi is very clever and surely never wrong.) If Deusovi is on the right, then again his statement would be wrong. But it is possible that Deusovi is in the centre.

And in this case

Deusovi is as usual in the role of person 3 above, and his hat is green.

• Correct! That's what the "knowledge" tag (as well as the fact that the puzzle's givens are contradictory without this piece of information) is supposed to hint at. Deusovi has mentioned on PSE multiple times that he's colourblind, and has told me that the two others in the question should know that he's colourblind and, to the best of his knowledge, that he's the only colourblind person on PSE. Commented May 20, 2017 at 18:44