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Re: [Phys-L] Inference Lab Design

Given three people and you can only see two of them. Now, everyone raised his hand meaning that those two other people saw someone with a white hat. So, because you saw someone with a black hat and someone with a white hat you would raise your hand... that means you have to have a white hat because otherwise the person you saw with the white hat would not have raised his hand because if you had a black hat he would see only two black hats.

On Aug 19, 2012, at 1:41 PM, Jeff Bigler wrote:

On 8/19/2012 2:29 AM, D.V.N. Sarma wrote:

Talking about inference, here is a story I have read somewhere
which some of you may be knowing already.

There is a society of logicians. Anybody who wants join the society
will be given a test and only those who pass the test
are admitted.

Once three new candidates applied for membership. The society
devised a test for them. They were told that they will be bindfolded
and three caps will be placed one each on their heads. The caps will
be either black or white. Then their blindfolds will be removed.
The candidate cannot see the color of the cap on his own head but
only of those on the heads of the other two. A candidates who sees
one or more white caps should rise his hand. From the hands raised
one has to guess the color of the cap on his own head.

The candidates were blindfolded and three white caps were placed on
their heads. The blindfolds were removed. All the three raised hands.
Presently one of them said that his cap is white. How did he guess that?

I must be missing something. Suppose the candidate who spoke up was
candidate #3 (C3). The following situations are both possible:

C1 C2 C3
cap white white white
hand raised raised raised

C1 C2 C3
cap white white black
hand raised raised raised

Jeff Bigler
Lynn English HS; Lynn, MA, USA
"Magic" is what we call Science before we understand it.
Forum for Physics Educators