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Home > Logic > Weights and Scales
One of Sixteen (Posted on 2015-12-29) Difficulty: 3 of 5
I have two sets of 8 coins. In one set the coins weigh 30g each, in the other set the coins weigh 31g each.
Unfortunately they got mixed together in one big pile of 16 coins. I want to identify one coin. It can be from either set.

(Easy) Using a balance scale, identify a coin in four weighings.

(Hard) Identify a coin in just three weighings.

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): What's the problem? (and a spoiler) | Comment 8 of 12 |
(In reply to re: What's the problem? (and a spoiler) by Brian Smith)

If it is not possible to identify a specific coin in just three weighings, then that explains why I did not come up with a method.  That, plus the fact that I only tried to do it in my head.


As expected, the easy method has fewer expected weighings (slightly more than half) when compared to the hard method.  The hard method always takes 3 weighings. 

My calculations of the easy method:
1 weighing   ~53.33% of the time
2 weighings ~38.97%
3 weighings ~ 7.68%
4 weighings ~ 0.02%
expected weighings: ~1.54

Edited on January 1, 2016, 10:36 am
  Posted by Steve Herman on 2016-01-01 10:34:53

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