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Classic counterfeit coin problem (Posted on 2005-06-04) Difficulty: 3 of 5
In the famous "The Odd Coin" problem you are given twelve coins, exactly one of which is lighter or heavier than the other coins. You are to determine the counterfeit coin, and whether it is lighter or heavier than the other coins, in just three weighings with a balance.

Can you solve this problem with the additional restriction that you must decide what coins go on each pan for all three weighings before any weighing takes place?

See The Solution Submitted by McWorter    
Rating: 3.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Another way to answer it | Comment 8 of 13 |
(In reply to Another way to answer it by Jennifer)

You're not assured that the odd one is lighter.  The odd one might be heavier.

Here's a table of the results of the weighings Ken Haley gives in his solution:

 1 light   rlr
 2 light   r==
 3 light   rrl
 4 light   rr=
 5 light   lrr
 6 light   lr=
 7 light   l=r
 8 light   l=l
 9 light   =lr
 10 light  =l=
 11 light  =ll
 12 light  ==l
 1 heavy   lrl
 2 heavy   l==
 3 heavy   llr
 4 heavy   ll=
 5 heavy   rll
 6 heavy   rl=
 7 heavy   r=l
 8 heavy   r=r
 9 heavy   =rl
 10 heavy  =r=
 11 heavy  =rr
 12 heavy  ==r

where l means the left pan goes down; r, the right; and = both pans balance.


  Posted by Charlie on 2005-06-05 17:43:52
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