12 coins balance scale

For fans of all other kinds of logic puzzles

12 coins balance scale

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 !
7b53
2012 Supporter

Posts: 156
Joined: 01 January 2012
Location: New York

Re: 12 coins balance scale

This is a very old story,

It took me some time to get back the solution
champagne
2017 Supporter

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Joined: 02 August 2007
Location: France Brittany

Re: 12 coins balance scale

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 ?
7b53
2012 Supporter

Posts: 156
Joined: 01 January 2012
Location: New York

Re: 12 coins balance scale

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
champagne
2017 Supporter

Posts: 5963
Joined: 02 August 2007
Location: France Brittany

Re: 12 coins balance scale

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.
7b53
2012 Supporter

Posts: 156
Joined: 01 January 2012
Location: New York

Re: 12 coins balance scale

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
champagne
2017 Supporter

Posts: 5963
Joined: 02 August 2007
Location: France Brittany

Re: 12 coins balance scale

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.
7b53
2012 Supporter

Posts: 156
Joined: 01 January 2012
Location: New York

Re: 12 coins balance scale

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

Bill Smythe
Smythe Dakota

Posts: 536
Joined: 11 February 2006

Re: 12 coins balance scale

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
champagne
2017 Supporter

Posts: 5963
Joined: 02 August 2007
Location: France Brittany

Re: 12 coins balance scale

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 ??
7b53
2012 Supporter

Posts: 156
Joined: 01 January 2012
Location: New York

Re: 12 coins balance scale

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?

Bill Smythe
Smythe Dakota

Posts: 536
Joined: 11 February 2006

Re: 12 coins balance scale

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?
ronk
2012 Supporter

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Joined: 02 November 2005
Location: Southeastern USA

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

Pat

Posts: 3506
Joined: 18 July 2005

Re:

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.
ronk
2012 Supporter

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Joined: 02 November 2005
Location: Southeastern USA

Re: 12 coins balance scale

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.
dobrichev
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