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Colorful foreheads


Best Answer CaptainEd, 30 January 2013 - 08:22 PM

Spoiler for notations, proof, and answer
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3 replies to this topic

#1 bonanova

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Posted 30 January 2013 - 07:32 PM

Variation on a familiar theme.

You and two other crack Denizens participate in a competition based purely on logic.
Not surprisingly, you win. But because of the large stakes involved, including but not
limited to the coveted bonanova gold star, a federal investigator has been assigned
to rule out any possible allegation of cheating. Think Slumdog Millionaire. Therefore
You are required to explain precisely how you were able to win.

Here are the facts.

The host, Rookie produced eight colored stamps: four red and four blue.
Two each were affixed to the foreheads of the three contestants.
The remaining two were placed in Rookie's pocket.
Each contestant can see the four stamps on the other two foreheads,
but none can see the colors on his/her forehead, nor the two in Rookie's pocket.

Rookie then asks the contestants in turn if they know their own colors.

A. No, I don't.
B. No, I don't.
C. No, I don't.
A. No, I don't.
B. Yes, I do.

You were contestant B.

How did you convince the investigators that there was no cheating?
For extra credit and the gold star, what were your colors?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 CaptainEd

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Posted 30 January 2013 - 08:22 PM   Best Answer

Spoiler for notations, proof, and answer

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#3 k-man

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Posted 30 January 2013 - 08:47 PM

Spoiler for pure logic and no cheating

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#4 bonanova

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Posted 30 January 2013 - 09:06 PM

You both have it.
CaptainEd got it first.
Congrats both.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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