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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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Solution it is possible!!!! | Comment 6 of 10 |

I believe it is possible to resolve the problem in 3 steps:

 <o:p></o:p>

step 1  arbitrary AB vs CD 

step 2  ...  AC vs BD

step 3        TBD by the outcomes of the  first  2 steps

 <o:p></o:p>

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

 <o:p></o:p>

 <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

 <o:p></o:p>

 <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

 <o:p></o:p>

 <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

 <o:p></o:p>

To assure that all cases are covered , the labeling A,B,C,D

should be done after step 2.

 <o:p></o:p>

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

 <o:p></o:p>

 <o:p></o:p>

-Please correct me if I am wrong<o:p></o:p>

 <o:p></o:p>


  Posted by Ady TZIDON on 2007-03-10 02:47:36
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