# Guess the hat colors - Riddle 5

I was impressed with all the answers and interesting reasoning in the previous puzzle (riddle 4). So for today I have another original hat guessing puzzle!

Challenge: guess who is wearing the green hats and the black hats

Rules:

1. The icons on the top of the image show that this time there are 2 "hatless" prisoners. The rest are wearing black and green hats, but you will have to figure out how many of each there are.
2. However, the 7 of them do know since the beginning how many hats of each color there are, it's just you who doesn't know.
3. The four first prisoners are facing the last three. They can see the hats that are in front of them, but not their own. (e.g.: B can see the the 5 hats from C to G, and E can see the 4 hats from D to A)
4. The three of them talk at the same time, and they give you a clue about how many hats they can see.
5. The hat of D is given, it is green. The rest can be any of the three types: hatless, green, or black

Please let me know what you think about this one, or if you have any ideas for new ones...and I wish you good luck!

We know that there are five hats in total, since two of 7 people are hatless, and that A can see an equal amount of hats of each color. Thus, he must be wearing a hat, and there are at least 2 of every color of hat.

Since B is missing one hat from those four, and he sees more Black hats than Green, he must be wearing a Green hat.

For F to be able to see double Green over Black, he must be able to see D and B's green hats, and only one Black hat. Since we know A is wearing a hat, it must be Black; and thus, C and E are hatless. This means F and G both must be wearing the Black hats that A and B can see.

A, F, and G's hats are Black. B and D are wearing Green hats. C and E are wearing no hat.

• Well you are a quick one aren't you?
– PDT
Commented Sep 22, 2020 at 2:14
• Have an upvote for beating me to the punch...
– PDT
Commented Sep 22, 2020 at 2:14