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Four Coins and Three Weighings (Posted on 2007-03-08) Difficulty: 3 of 5
You have four coins to sort with a standard balance scale. Their weights are 20g, 21g, 22g and 23g. Prove that there is no strategy which can guarantee sorting the coins with only three weighings.

See The Solution Submitted by Brian Smith    
Rating: 4.3333 (3 votes)

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re(2): Information theory way | Comment 5 of 10 |
(In reply to re: Information theory way by Charlie)

There is only one grouping (A with D and B with C) which produces an equal weighing. If you used this weighing in your results, you would only use it once. Thus, in every group of 3 (rational) weighings, equal only will appear once, showing that you can only get at most 12 different results.


  Posted by Gamer on 2007-03-09 11:43:25
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