Can You Tell Me The Color of My Own Hat?

Logic Level 1

Three people $A, B,$ and $C$ are sitting on stairs one after another such that $C$ on the first stair cannot see the two above him and $B$ on the second stair cannot see the one above him. There are 2 red and 2 white hats available and each person is wearing one of them. However, no one knows the color of their hat.

The following conversation then took place between $A$ and $B$ :

$A:$ I don't know which color hat I'm wearing.
$B:$ At first I didn't know, but I know the color of my hat now.

If $C$ is wearing a red colored hat, what color hat is $B$ wearing?

Red White Cannot be determined This is an impossible scenario

3 solutions

Mateo Matijasevick
May 19, 2016

Relevant wiki: K-level thinking

As $A$ does not know which colour hat is he wearing, $B$ and $C$ are wearing a red hat and a white hat in some order; if both of them are wearing the same colour hat, then $A$ would know which colour hat does he wear, as there are only $2$ hats of each colour. Since $C$ is wearing a red hat, $B$ must be wearing a white hat.

Jackson.A.Roberts 2020
Feb 24, 2017

As $A$ is saying he has no idea about what color hat he has, that means because we know $C$ has a red hat, B has a white hat, therefore proving impossible to $A$ to determine his hat color. $B$ knows after $A$ said that, because he can see $C$ has a red hat, and $A$ cannot determine his hat color, that his hat is white. If $B$ 's hat was red, $A$ would've known his hat was white, therefore proving his statement false.

Karan Shah
May 19, 2016

How does C know which color hat he is wearing.. In the conversation how can he say he knows which hat he is wearing..

It is stated that C HAS a red hat. But it is not stated that C knows what color of his hat.

Marc Ballon - 5 years ago

Because $B$ said "At first I didn't know but I know the colour of my hat now."

Mateo Matijasevick - 5 years ago

According to my understanding.. C should just know that the color of Bs hat and Cs hat is different.. He cant see any of the other hat to come to a conclusion about which colir har he is wearing..

karan shah - 5 years ago

I have got the answer right.. And theres no doubt in the solution which you gave.. But i have a doubt in the question.. In which C says that he knows the colour of his hat.. How does he come to know about it?

karan shah - 5 years ago

You are right. Nice reasoning!

Ammarah Ehsan - 5 years ago

Mmm ok, got it. @Ammarah Ehsan should delete what C says.

Mateo Matijasevick - 5 years ago

@Mateo Matijasevick – Agreed. Its not important to the question... (Except as a red herring maybe? (no pun intended) ) and it appears to be wrong... Nice problem, though! (+1)

Geoff Pilling - 5 years ago

Can You Tell Me The Color of My Own Hat?

3 solutions

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