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Lose your marbles

 
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lielay
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PostPosted: Tue Nov 01, 2005 9:31 pm    Post subject: Lose your marbles Reply with quote

This is one of my favorites:

You have twelve marbles. Eleven of the marbles are of equal weight, but one is heavier or lighter. You have a balancing scale you can use to find this marble and figure out if it weighs more or less than the others. How can you find the defect marble in just 3 weighings?
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Smert



Joined: 31 Oct 2005
Posts: 11
Location: Gainesville, FL

PostPosted: Thu Nov 03, 2005 4:50 am    Post subject: Reply with quote

Answer follows, in white.
Measurement 1: Split the dozen into two piles of six, measure, keep the heavier group of six.

Measurement 2: Split the six into two groups of three, measure, keep the heavier group.

Measurement 3: Compare any two marbles. If one turns out to be heavier, bingo! If they're equal then the one you didn't compare is the ugly duckling.


Or did I miss something?
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Michael Chu



Joined: 10 May 2005
Posts: 1631
Location: Austin, TX (USA)

PostPosted: Thu Nov 03, 2005 7:01 am    Post subject: Reply with quote

Smert,

The answer doesn't work because you don't know if the defective marble is heavier or lighter. The problem is a little trickier. Smile

This is also one of my favorite puzzles. Thanks for posting it lielay!
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Smert



Joined: 31 Oct 2005
Posts: 11
Location: Gainesville, FL

PostPosted: Sat Nov 05, 2005 3:22 am    Post subject: Reply with quote

D'oh! I missed the part that said it could be lighter. . .time to rethink the problem. . .
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pp-guest
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PostPosted: Fri Jun 02, 2006 2:29 am    Post subject: 12 marbles - solution site Reply with quote

I did not come up with the answer but found a place which has it. Quite intricate for a seemingly simple problem.
http://home.att.net/~numericana/answer/weighing.htm#weighing
Good work Mike Chu - I stumbled on your site looking for a way to make Almond extract juice for my little kid - any pointers?
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cosmiclobster
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PostPosted: Sun Jan 07, 2007 7:38 am    Post subject: Reply with quote

Wow, god one!! I started with the same number of marbles on each side as the solution, but then decided I didn't want to spend the next several hours working out the possibilities so I cheated and went right to the answer. If I had started this puzzle early on a Sunday morning, things might have been different!! Big smile
Thanks for sharing!
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youngcook



Joined: 11 Apr 2007
Posts: 97
Location: GA

PostPosted: Thu Apr 12, 2007 3:32 pm    Post subject: WHOA! Reply with quote

Nice,lielay. Very tricky. I had to "cheat "too. After 2 days of thinking! Thank you so much for sharing.
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MindShock
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PostPosted: Tue Jun 26, 2007 9:48 pm    Post subject: Solution Reply with quote

Here's a solution that will probably amaze you, once you understand it :-)

You make 3 fixed weighings with each independend of the result of the previous weighing. It goes as follows:

1st weighing: 5,6,8,10 --- 7,9,11,12
2nd weighing: 2,3,4,7 --- 5,6,11,12
3rd weighing: 1,4,10,11 --- 2,5,7,8

Now you have to know that the first 1st weighing has a "score" of 9 or -9 points. The 2nd one scores 3 or -3 points, the third scores 1 or -1 point.

To test this, we choose any marble, lets say no. 8, and we say its lighter than the others. In 1st weighing the right side of the balance will go down then, so you have to keep the score "-9" in mind for that. 2nd weighing will stay balanced so "0" points for that. In 3rd weighing the right side will go up, so "+1" for that. Now we add up our scores of -9+0+1 and the result is -8, which means it was marble no. 8 and its lighter than others.

It works like this for all other numbers, so there you have your solution!

The only exception are numberes 7,9,11,12 for which the result is reversed (this is because you have to place 4 marbles on the right side as well in the first weighting). So let's say its marble 11 which is heavier than others you would get "-9" in 1st weighing (right side goes down). 2nd weighing "-3" (right side goes down). 3rd try is "+1" (right side goes up). The result will be -11 and since this is one of the numbers mentioned above you, just reverse the result to +11 and know that its heavier than the others.
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