# Guess the hat colors - Riddle 2

After the previous riddle I asked was resolved so quickly, I propose you another self-created hat-guessing riddle. This time it is slightly more difficult, good luck!

TASK: You have to guess which ones are wearing green hats and which ones are wearing black:

DESCRIPTION: Each one can see 2 hats, the one on their right and the one on their left, but they can't see their own.

Pay attention to the order, they give tips one by one:

1- F sees 2 hats, 1 of them is green (the other one must be black then)

2- After listening to A, C figures out which hat he must be wearing (he doesn’t know before listening to F)

3,4,5- They wait to talk after C, and they all confirm they see only 1 green hat next to them

You don’t know how many green and black hats there are of each color (6 in total, all of them must be wearing one), but they do know how many hats there are of each color. For example, if B were the only black hat, C would know his hat is green, before even listening to F (so the answer would be wrong)

We already know B is wearing a black hat. You have to guess the other 5 hats! Of course, there is only one possible solution

I believe the answer is:

A - Green
B - Black
C - Green
D - Black
E - Black
F - Green

Reasoning:

We start with knowing B is black. With that, even out of order we know that F must be green because of A. Given that we know that D must be black since E can only see 1 green (F) Now we know C can only see two blacks, and he knows that F can only see one black. The only way he can now know his own hat is if there are 3 green hats and 3 black hats. He knows F can only see one, he can't see any, so he and F must both have the other two green hats. Since C is green, and D can only see 1 hat, E must be black and A must be the last remaining green.

• You beat me to it. You can deduce a lot from their factual statements - there are only two colour arrangements that fit - and then only one of those possibilities allows C to have deduced his hat. Commented Sep 18, 2020 at 15:13