12 coins balance scale

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12 coins balance scale

Postby 7b53 » Sun Sep 16, 2012 3:35 am

one of the 12 coins has a different weight.
you are given a balance scale.
you are allow only to use it 3 times.

the difficult part is that the coin could be either lighter or heavier.
it is not given.

remember to apply all scenarios !
and please try to solve it manually .

have fun !
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Re: 12 coins balance scale

Postby champagne » Tue Sep 18, 2012 3:11 pm

This is a very old story,

It took me some time to get back the solution
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Re: 12 coins balance scale

Postby 7b53 » Tue Sep 18, 2012 7:57 pm

yes, indeed...an old one. champagne;
does it make us feel 30 yrs younger...

with the computer these day, it might have another solution.
or can it have more than one solution ?
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Re: 12 coins balance scale

Postby champagne » Tue Sep 18, 2012 10:05 pm

7b53 wrote:yes, indeed...an old one. champagne;
does it make us feel 30 yrs younger...

with the computer these day, it might have another solution.
or can it have more than one solution ?


It takes at worth some hours to figure out the solution (some will answer in some minutes), and likely several days to work out a program to do the same.

There is not much room for several really different solutions
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Re: 12 coins balance scale

Postby 7b53 » Wed Sep 19, 2012 2:07 am

It takes at worth some hours to figure out the solution (some will answer in some minutes), and likely several days to work out a program to do the same.

There is not much room for several really different solutions


I was told the record solving-time at some college was ~45 mins.

perhaps there is no more ways but for only one solution.
(assuming ours are the same) manually, i don't see another.
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Re: 12 coins balance scale

Postby champagne » Wed Sep 19, 2012 5:47 am

I think one request is missing in your first post.

The player must say at the end if the false coin is heavier or lighter.
Then, you have only very similar possibilities to solve the problem
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Re: 12 coins balance scale

Postby 7b53 » Thu Sep 20, 2012 4:04 am

champagne wrote:The player must say at the end if the false coin is heavier or lighter.


this might actually causes confusion.
and how is it possible ?

all depending the outcome of the scale...
it can be lighter or heavier.
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Re: 12 coins balance scale

Postby Smythe Dakota » Fri Sep 21, 2012 7:34 am

OK, this banter has been going on long enough now. It's about time for somebody to post a spoiler.

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Re: 12 coins balance scale

Postby champagne » Fri Sep 21, 2012 8:40 am

Smythe Dakota wrote:OK, this banter has been going on long enough now. It's about time for somebody to post a spoiler.

Bill Smythe


just make a search on google with "12 coins scale", you'll get 30 millions answers including a wikipedia complete analysis of that old problem
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Re: 12 coins balance scale

Postby 7b53 » Sun Sep 23, 2012 4:39 am

this is no fun... now the solution is everywhere.
...how about...81 coins with the same problem.
does anyone know the number of scale allow ??
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Re: 12 coins balance scale

Postby Smythe Dakota » Thu Sep 27, 2012 5:35 am

How about a generalization?

For any positive integer N, what is the smallest number W of weighings that is guaranteed to find the false coin?

Apparently, for N=12, W=3.

And, what is the smallest number X of weighings that is guaranteed not only to find the false coin, but also to determine whether it is lighter or heavier than the others?

Obviously, for each N, X is greater than or equal to W. Does X ever equal W, or is X always greater?

Are these functions monotone? Or are there cases where, if N is increased, W decreases?

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Re: 12 coins balance scale

Postby ronk » Thu Sep 27, 2012 1:03 pm

Smythe Dakota wrote:... what is the smallest number X of weighings that is guaranteed not only to find the false coin, but also to determine whether it is lighter or heavier than the others?

Obviously, for each N, X is greater than or equal to W. Does X ever equal W, or is X always greater?

I can't envision a scenario where the false coin is found without knowing whether it is lighter or heavier. Does anyone have an example?
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Postby Pat » Thu Sep 27, 2012 1:18 pm

ronk wrote:I can't envision a scenario where the false coin is found without knowing whether it is lighter or heavier. Does anyone have an example?

4 coins

first weigh A:B
next weigh A:C

if D is the fake, we don't know if it is light or heavy
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Re:

Postby ronk » Thu Sep 27, 2012 2:12 pm

Pat wrote:
ronk wrote:I can't envision a scenario where the false coin is found without knowing whether it is lighter or heavier. Does anyone have an example?

4 coins

first weigh A:B
next weigh A:C

if D is the fake, we don't know if it is light or heavy

I guess that works, but it doesn't verify that a false coin actually exists. Much like trusting that a sudoku puzzle has only one solution.
Last edited by ronk on Thu Sep 27, 2012 2:15 pm, edited 1 time in total.
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Re: 12 coins balance scale

Postby dobrichev » Thu Sep 27, 2012 2:13 pm

For 1 coin the false one is determined by 0 weightings, but it is impossible to determine whether it is lighter or heavier.
For 2 coins if it is not known the deviation direction, the problem is unsolvable.
For infinitely large number of coins, infinitely large number of weightings are required.
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