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.
I believe it is possible to resolve the problem in 3 steps:
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step 1 arbitrary AB vs CD
step 2 ... AC vs BD
step 3 TBD by the outcomes of the first 2 steps
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if AB > CD and AC > BD A =23 D=20
and step 3 will be B vs C
to find out whether B =21 AND C=22 or vice versa
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<o:p></o:p>
if AB > CD and AC < BD B =23 D=20
and step 3 will be A vs C <o:p></o:p>
to find out whether A =21 AND C=22 or vice versa
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<o:p></o:p>
if AB > CD and AC = BD A =23 C=20
and step 3 will be B vs D <o:p></o:p>
to find out whether D =21 AND B=22 or vice versa
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<o:p></o:p>
if AB = CD and AC > BD A =23 B=20
and step 3 will be D vs C
to find out whether D =21 AND C=22 or vice versa
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To assure that all cases are covered , the labeling A,B,C,D
should be done after step 2.
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Counting all the possible results ( 2*3*3=18) is not enough to label the problem as unsolvable- we are not sorting
4 entities with no data about their weights :
the additional info that helps is: <o:p></o:p>
only one partition in two equal subsets is possible i.e. -20,23 vs 21,22
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-Please correct me if I am wrong<o:p></o:p>
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it is possible!!!!
