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 Four Coins and Three Weighings (Posted on 2007-03-08)
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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 All things being equal | Comment 9 of 10 |
I think you forgot the cases A, B =21, 22, C=23 D=20 the step AB=CD AC>BD Thus, if AB=CD AB>CD, the cases to consider are (in order A,B,C,D)

23 20 22 21
22 21 23 20
20 23 22 21
22 21 20 23

Then you have 4 possibilities and only two possible results. Doing anything different after AB=CD wouldn't change this problem, as you would have 8 possibilities if AB=CD (ie the arbitrary first weighing results in it being equal)

Due to equality being commutative, you can't favor one side over the other, so after AB=CD and {AC>BD, AC<BD} all that is known is that A or C is 20, and B or D is 23.

 Posted by Gamer on 2007-03-10 14:55:51

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