Yet more hat logicians

Logic Level 2

In a box, there are three red and two green hats. Four logicians—Alice, Bob, Carol, David—pick one hat each from the box without looking and put them on.

Each of them can see the hats everyone else is wearing but not their own. They have the following conversation:

Alice: "I know the color of my hat."
Bob: "I am wearing a red hat."
Carol: "I am wearing a green hat."

What is the color of David's hat?

Green Red Insufficient information

2 solutions

X X
Apr 8, 2018

Alice knows the color of her hat.
1.If she wears red,then there must be two other people wearing green.
2.If she wears green,the three other people must be wearing red,but Carol is wearing green,so it must be the first case.
There is two people wearing green,one is Carol,so the other one is David.

But then how would Carol know that her hat is green?

Siva Budaraju - 3 years, 2 months ago

Because she sees Alice's hat is red,and Alice knows the color of her hat.So she knows it's the first case,two people wearing green.But she only sees David wearing green,so she knows that she is the other one wearing green.

X X - 3 years, 2 months ago

Oh, I see. Thanks!

Siva Budaraju - 3 years, 2 months ago

Naren Bhandari
Apr 13, 2018

$\large {\color{#D61F06}\text{3 red hats}} \qquad {\color{#20A900}\text{2 green hats}}$ Carol wears green hat , Bob wears red hat since they can see each other's not their own. So either Alice or David should be wearing green hat.

Remaining hats : $\large {\color{#D61F06}\text{2 red hats}} \qquad {\color{#20A900}\text{1 green hat}}$ Note that Alice said she knows her hat's color . She can only be sure about her hat if hats remaining are in like pairs (red,red) or (green ,green) but not (red,green) which is seems to happen if David wears green hat then hats we are left are only like in pairs(red,red). So David wears green hat.

Yet more hat logicians

2 solutions

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