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smellycheeseboy
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Joined: 15 May 2003
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 Posted: Mon Jun 27, 2005 7:16 pm Post subject: An interesting brain teaser |
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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
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xaenn
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Joined: 21 Oct 2004
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| Posted: Mon Jun 27, 2005 9:03 pm Post subject: |
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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
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Joined: 31 Jan 2004
Posts: 218
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| Posted: Mon Jun 27, 2005 9:28 pm Post subject: |
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| Place counterfeit detection apparatus in / on the scales. |
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resolute
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Joined: 22 Jan 2005
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Location: Texas, USA
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| Posted: Mon Jun 27, 2005 9:34 pm Post subject: |
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| 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.
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Valhlalla
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Joined: 21 Sep 2003
Posts: 161
Location: Sydney, Australia.
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| Posted: Mon Jun 27, 2005 10:21 pm Post subject: |
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I can get it to work with 3 but only if the first weighing is balanced.
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smellycheeseboy
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Joined: 15 May 2003
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| Posted: Mon Jun 27, 2005 11:12 pm Post subject: |
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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
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xaenn
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Joined: 21 Oct 2004
Posts: 23
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| Posted: Mon Jun 27, 2005 11:54 pm Post subject: |
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| Yeah, needless to say I would've never figured that out. |
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doubleagent
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Joined: 14 Apr 2005
Posts: 370
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| Posted: Tue Jun 28, 2005 12:48 am Post subject: |
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| Valhlalla wrote: | | I can get it to work with 3 but only if the first weighing is balanced. |
Same here. gonna read.
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beu
Retired Dev
Joined: 03 Mar 2004
Posts: 22
Location: London, UK
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| Posted: Tue Jun 28, 2005 3:18 am Post subject: Re: An interesting brain teaser |
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Interesting ?!  |
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richardjames
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Joined: 04 Jan 2005
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Location: Manchester, UK
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| Posted: Tue Jun 28, 2005 4:33 am Post subject: |
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We once got a load of these as a University assignment to encourage lateral thinking or something, I will try and dig them out...
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smellycheeseboy
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| Posted: Sun Jul 03, 2005 11:12 pm Post subject: |
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As soon as I stop being lazy I will post a much easy solution that I found. Until then you can rack your brains.
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andrewd18
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pjp
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| Posted: Sun Jul 03, 2005 11:33 pm Post subject: |
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A slight variation: http://www.cartalk.com/content/puzzler/transcripts/200353/answer.html
Could've sworn this thread's version had already been posted.
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tln
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Joined: 24 Sep 2003
Posts: 1502
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| Posted: Sun Jul 03, 2005 11:43 pm Post subject: |
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| IIRC a variation of this test is/was used by IBM during job interviews. |
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stevenaleach
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Joined: 18 May 2005
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| Posted: Mon Jul 04, 2005 7:46 pm Post subject: |
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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
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Joined: 25 Feb 2003
Posts: 333
Location: Aberdeen, Scotland
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| Posted: Mon Jul 04, 2005 9:08 pm Post subject: |
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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
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Joined: 18 May 2005
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| Posted: Tue Jul 05, 2005 12:05 am Post subject: |
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| 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
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Joined: 07 Apr 2005
Posts: 912
Location: Brussels, Belgium
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| Posted: Tue Jul 05, 2005 4:08 am Post subject: |
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| 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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