Logical question

King and three prisoners King said: Everybody is wearing a hat, a hat is either black or white. The prisoners can see each other and can see other people's hat color, but can not see the color of his own hat. No speaking is allowed. King actually gave them wearing a black hat. And set the following rules: 1 The prisoners who saw two other people are white hat, can be released. (2) knows his black hat, can be released. After some time, A prisoner finds his hat is black and was released, how did he do so?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Let's call the prisoners $A$ , $B$ and $C$ . Prisoner $A$ sees that prisoners $B$ and $C$ both wear a black hat. If prisonar $A$ would wear a white hat, then prisoner $B$ would know after some time that he wore a black hat, because if he would also wear a white hat, prisoner $C$ would be released, because he'd see two other white hats. But prisoner $B$ doesn't say anything, so prisoner $A$ knows that he doesn't wear a white hat but a black hat, so he is released. I hope that makes sense.

Tim Vermeulen - 7 years, 10 months ago

he knows that if the other two are black then his must be black because no one can see the two whites or the king is lieing

Abdul Rahman Syed - 7 years, 10 months ago

Not quite

Jason Kang - 7 years, 10 months ago

You should click the Reply button under the comment you want to reply to, otherwise it wouldn't make much sense if there are multiple other comments.

Tim Vermeulen - 7 years, 10 months ago

They write in the dirt OR they take off their hats

Daniel Leong - 7 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$