Interesting Puzzle

[PairTheBoard]

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Forgive me if this has been posted or if it is trivially easy. I found it interesting.

Your are given 12 marbles, identical in appearance. Exactly one marble has a mass either slightly more OR slightly less than the other 11 (the difference is so minimal no human could possibly detect it without the use of scientific equipment). You are given a balance and allowed to use it exactly 3 times. You must determine which marble has a slightly different mass and whether it has more or less mass than the other 11. How do you do it?

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I saw a more difficult version of this problem where you are not allowed to base your measurements on the result of previous measurements. Everything else is the same.

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I find it hard to believe it can be done with just 3 predefined weighings.

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[NutzyClutz]

Get an aquarium. Put the marbles in. Fill with water. Add salt slowly. If the marble is light, it will be only marble to rise. If marble is heavy. It will be only marble not to rise.

Line up the marbles in a wind tunnel slowly increase wind....

Put each marble, in US Golf Assoc. testing machine... The marble the is driven the "odd" distance ...

Fire pairs of marble at each other headon, the marble pair that doesnt rebound equally has the "odd marble". Take one of these marbles, and fire it with one of the other 10 marbles, if it rebounds equally, the marble you didnt select is the "odd marble". Otherwise, the marble you selected is the "odd marble"

Sandblast each marble. Measure the amount of sand used for each one. The odd amount of sand is the "odd marble"


Attach 1 marble to each side of a precision dice. Roll die 10,000,000 times to determine dice bias. The number that came up most, the odd marble is either attached to that side, or on the opposite side. Take one of these marbles, and attach it to coin. Take one of the other 10 marbles, and attach it to other side of coin. Flip 10,000,000. If the coin is biased, then the marble you selected is the "odd marble", if not biased. the marble you did not select is the "odd marble"

Hook up the marbles as follows
web page
Coax the person who knows the answer into state of hypnosis...

[PairTheBoard]

I have not looked at the comments yet and am still thinking about this one.

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[PairTheBoard]

Ok, I think I finally got this while falling asleep last night.

Begin White:
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First weight 4-4.
If they balance you're left with 4. Weigh 3 of those against 3 standards. If they balance, weigh the 4th against a standard. If they don't balance, weigh two of them against each other.

If the 4-4 don't balance you know either One 4-group is light or the other 4-group is heavy. Here's the tricky one. Put 3 lights and two heavies on the left scale. Weigh against 4 standards and 1 light on the right. If they balance you'll be left with 2 heavies which are easy. If the left is light you know it's the 3 lights on the left which you handle like above. If the left is heavy you know it's either the two heavies on the left or the one light on the right. Weigh the two heavies against each other and you're done.
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End White


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