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smellycheeseboy Apprentice
Joined: 15 May 2003 Posts: 263 Location: The Future

Posted: Tue Jun 28, 2005 12:16 am Post subject: An interesting brain teaser 


You have 12 coins, one of which is counterfeit. The counterfeit coin is either heavier or lighter than the other 11 coins.
You have to weigh the coins on a balance scale to determine which coin is the counterfeit coin.
What is the minimum number of weighings that you have to do in order to GUARANTEE that you have found the counterfeit coin and is it heavier or lighter?
I know the answer to this but I don't know how to get there so good luck.
Me _________________ "No amount of fear can stop the rise of free media, or free software." Jonathan Schwartz, Sun Microsystems 

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xaenn n00b
Joined: 21 Oct 2004 Posts: 23

Posted: Tue Jun 28, 2005 2:03 am Post subject: 


1. First put 6 on each side.
2. Take the lighter side of 6 and split it in half.
3. Assume the worst case scenario that it balances. and split the other pile of 6 in half.
4. See which pile of three is lighter.
5, Compare two of the coins
6. Compare two more of the three coins (one repeat). You now know if both balanced, that's the worst case scenario so assume they do.
7. Take two from the other stack of three and compare them.
8. Compare two more from that stack of three (one repeat)
It should now be clear which coin is different and if it is heavier or lighter. 

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myuser Apprentice
Joined: 31 Jan 2004 Posts: 218

Posted: Tue Jun 28, 2005 2:28 am Post subject: 


Place counterfeit detection apparatus in / on the scales. 

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resolute n00b
Joined: 23 Jan 2005 Posts: 29 Location: Texas, USA

Posted: Tue Jun 28, 2005 2:34 am Post subject: 


xaenn wrote:  1. First put 6 on each side.
2. Take the lighter side of 6 and split it in half.
3. Assume the worst case scenario that it balances. and split the other pile of 6 in half.
4. See which pile of three is lighter.
5, Compare two of the coins
6. Compare two more of the three coins (one repeat). You now know if both balanced, that's the worst case scenario so assume they do.
7. Take two from the other stack of three and compare them.
8. Compare two more from that stack of three (one repeat)
It should now be clear which coin is different and if it is heavier or lighter. 
The minimum number of weighings is three. Back to the drawing board for you.
HINT: think about what you can do with three piles of four coins. _________________ "Our Nation  this generation  will lift a dark threat of violence from our people and our future. We will rally the world to this cause by our efforts, by our courage. We will not tire, we will not falter, and we will not fail." 

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Valhlalla Apprentice
Joined: 22 Sep 2003 Posts: 161 Location: Sydney, Australia.

Posted: Tue Jun 28, 2005 3:21 am Post subject: 


I can get it to work with 3 but only if the first weighing is balanced. _________________ Pork Chop Sandwiches, Oh Sh*t! 

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smellycheeseboy Apprentice
Joined: 15 May 2003 Posts: 263 Location: The Future

Posted: Tue Jun 28, 2005 4:12 am Post subject: 


Here is a link to a pretty good explanation of the answer:
http://home.att.net/~numericana/answer/recreational.htm#weighing
Its tougher than you think. I had to cheat to get it.
Me _________________ "No amount of fear can stop the rise of free media, or free software." Jonathan Schwartz, Sun Microsystems 

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xaenn n00b
Joined: 21 Oct 2004 Posts: 23

Posted: Tue Jun 28, 2005 4:54 am Post subject: 


Yeah, needless to say I would've never figured that out. 

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doubleagent Guru
Joined: 15 Apr 2005 Posts: 444 Location: 127.0.0.1

Posted: Tue Jun 28, 2005 5:48 am Post subject: 


Valhlalla wrote:  I can get it to work with 3 but only if the first weighing is balanced.  Same here. gonna read. _________________
shickapooka wrote:  i think they programmed [otw] based on a rightwing jewishniggernazi, his gay, retarded, leftwing love slave with webbed feet, and their three headed cat that poops uncontrollably. the cat is also an apple fanboy 


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beu Retired Dev
Joined: 03 Mar 2004 Posts: 22 Location: London, UK

Posted: Tue Jun 28, 2005 8:18 am Post subject: Re: An interesting brain teaser 


Interesting ?! 

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richardjames n00b
Joined: 04 Jan 2005 Posts: 23 Location: Manchester, UK

Posted: Tue Jun 28, 2005 9:33 am Post subject: 


We once got a load of these as a University assignment to encourage lateral thinking or something, I will try and dig them out... _________________ Love is a snowmobile racing across the tundra and then suddenly it flips over, trapping you underneath. At night, the ice weasels come. 

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smellycheeseboy Apprentice
Joined: 15 May 2003 Posts: 263 Location: The Future

Posted: Mon Jul 04, 2005 4:12 am Post subject: 


As soon as I stop being lazy I will post a much easy solution that I found. Until then you can rack your brains. _________________ "No amount of fear can stop the rise of free media, or free software." Jonathan Schwartz, Sun Microsystems 

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andrewd18 Guru
Joined: 11 Apr 2004 Posts: 364 Location: Wisconsin, USA


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pjp Administrator
Joined: 16 Apr 2002 Posts: 16716


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tln Veteran
Joined: 24 Sep 2003 Posts: 1501

Posted: Mon Jul 04, 2005 4:43 am Post subject: 


IIRC a variation of this test is/was used by IBM during job interviews. 

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stevenaleach n00b
Joined: 18 May 2005 Posts: 19

Posted: Tue Jul 05, 2005 12:46 am Post subject: 


Another variant:
You have five stacks of coins, with 25 coins in each stack. One or more of the stacks may be counterfeit, but you don't know which one or ones. In fact, they could *all* be counterfeit or all legitimate. Your only guarantee is that the stacks are not mixed: that is each stack contains either all real or all counterfeit coins. A normal coin weighs 5 grams, whereas a counterfeit coin weighs 6 grams.
With just one weighing, you can determine which are counterfeit or real.
How? 

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stustill Guru
Joined: 25 Feb 2003 Posts: 333 Location: Aberdeen, Scotland

Posted: Tue Jul 05, 2005 2:08 am Post subject: 


Assuming the stacks are numbered 1  n, take 2^n coins from each stack and weigh them. Assuming all of the stacks are legitimate this should weigh 155 grams. Deduct 155 from the actual weight and convert the answer into binary. If the LSB is 1 then stack 1 is counterfeit, if the second LSB is 1 then stack 2 is counterfeit etc.
I think that works.... might be a brain fart though!
Stu 

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stevenaleach n00b
Joined: 18 May 2005 Posts: 19

Posted: Tue Jul 05, 2005 5:05 am Post subject: 


Quote:  Assuming the stacks are numbered 1  n, take 2^n coins from each stack and weigh them. Assuming all of the stacks are legitimate this should weigh 155 grams. Deduct 155 from the actual weight and convert the answer into binary. If the LSB is 1 then stack 1 is counterfeit, if the second LSB is 1 then stack 2 is counterfeit etc. 
That was it. Damn that was quick 

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aidy l33t
Joined: 07 Apr 2005 Posts: 915

Posted: Tue Jul 05, 2005 9:08 am Post subject: 


resolute wrote:  xaenn wrote:  1. First put 6 on each side.
2. Take the lighter side of 6 and split it in half.
3. Assume the worst case scenario that it balances. and split the other pile of 6 in half.
4. See which pile of three is lighter.
5, Compare two of the coins
6. Compare two more of the three coins (one repeat). You now know if both balanced, that's the worst case scenario so assume they do.
7. Take two from the other stack of three and compare them.
8. Compare two more from that stack of three (one repeat)
It should now be clear which coin is different and if it is heavier or lighter. 
The minimum number of weighings is three. Back to the drawing board for you.
HINT: think about what you can do with three piles of four coins. 
It's you that should go back to primary school, because the _maximum_ number of weighings is three. 

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