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airship
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In my day, I have driven
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There is a new logic puzzle going around among mathematicians that I found very interesting. Here's one version of it:

Quote:
Three contestants, Alice, Bob, and Cedric, enter a room and a hat is placed on each contestant's head so that he or she can't see it. The color of each hat is based on a coin toss – blue (B) for heads, red (R) for tails. After all the contestants enter the room, they look at the colors of the others' hats and, based on this information, they guess the color of their hat. (NOTE: Simultaneously, without communicating.) They can guess red or blue, or, if they can't make up their mind, they can pass. No communication is allowed during the competition, but the players are allowed to agree on a strategy before play begins. The team wins if at least one of them guesses correctly, and none of them guesses incorrectly. What is the team's best strategy?


Of course, a random guess by one person while the other two pass gives them a 50/50 chance. But they can do MUCH better. How?

For the solution, go to the web site this quote was taken from:
http://www.daviddarling.info/encyclopedia/H/Hat_Problem.html

For more information on induction puzzles (of which the above is an example), see the Wikipedia article at:
http://en.wikipedia.org/wiki/Induction_puzzles
'The central secret of conjuring is a manipulation of interest.' - Henry Hay
Slim King
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Eternal Order
Orlando
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Didn't we do this one before? With the Dwarves in the dungeon?
I liked that one. Used it in my brothers high school class Smile
Here it is
http://www.themagiccafe.com/forums/viewt......1&16
THE MAN THE SKEPTICS REFUSE TO TEST FOR ONE MILLION DOLLARS.. The Worlds Foremost Authority on Houdini's Life after Death.....
airship
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In my day, I have driven
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Similar, but a different set of information. In the dwarf puzzle, each dwarf could only see the hats of the dwarves in front of him. In this one, each can see the hats of everyone else, but not his own.
'The central secret of conjuring is a manipulation of interest.' - Henry Hay
stanalger
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St. Louis, MO
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Also: In the dwarf puzzle, the dwarves didn't have the option
of passing.
Slim King
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Orlando
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I see, said the blind man Smile
THE MAN THE SKEPTICS REFUSE TO TEST FOR ONE MILLION DOLLARS.. The Worlds Foremost Authority on Houdini's Life after Death.....
Slim King
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What would be wrong with this....
We are not told in what order the contestants are to guess. Let's say that A,B, and C but not nessisarily in that order
say . After 2 seconds if A see's that B and C are the same color He will Pass. Thus B will know that his hat is the same color as C's and they will win.
If they are not, A will say nothing.
If, after 3 seconds, B see's that A and C are the same color, he will say Pass, and the C will know that his hat is the same color as A's.
If A and C are not the same, he says nothing ........
and C will know that his hat is the opposite color of A's hat.

NEVERMIND>>>I JUST SAW SIMULTANEOUSLY...
Mine would take five seconds or less.
However, I don't see that word "simultaneously"on the original challenge...???? Smile
THE MAN THE SKEPTICS REFUSE TO TEST FOR ONE MILLION DOLLARS.. The Worlds Foremost Authority on Houdini's Life after Death.....
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